Browse Function problems Studdy Solved!

Problem 1501

The function $f(x)=9 x+7 x^{-1}$ has one local minimum and one local maximum. This function has a local maximum at $x=$ $\square$ with value $\square$ and a local minimum at $x=$ $\square$ with value $\square$

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Problem 1502

$f(x)=\frac{2 x+2}{x^{2}-1}$
Answer Attempt 1 out of 2
Horizontal Asymptote: $y=$ $\square$ No horizontal asymptote $\square$ Vertical Asymptote: $x=$ No vertical asymptote $\qquad$ $x$ -Intercept: $\square$ ,0) $\square$ No $x$ -intercept $y$ -Intercept: (0, $\square$ ) No $y$ -intercept
Hole: $\square$ , $\square$ No hole $\square$

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Problem 1503

Question 7
An exponential function $f(x)=a \cdot b^{x}$ passes through the points $(0,7000)$ and $(3,56)$ . What are the values of $a$ and $b$ ? $a=$ $\square$ and $b=$ $\square$

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Problem 1504

Plot all of the existing five features of the following rational function (some may not be needed). If you get a fraction or decimal then plot as close to the true location as possible. $f(x)=\frac{-3 x-9}{x^{2}-2 x-15}$
Plot Rational Function Vertical Asymptote Horizontal Asymptote x-Intercept y-Intercept Hole

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Problem 1505

Period: DUE: Tuesdav, 11/19/24
1. Find the volume of the solid obtained by rotating the region given about the x -axis and using the given bounds. Sketch a picture of the graph. $y=0.3 x^{3}$ , the $x-$ axis, and $x=3$

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Problem 1506

Period: DUE: Tuesdav, 11/19/24
1. Find the volume of the solid obtained by rotating the region given about the x -axis and using the given bounds. Sketch a picture of the graph. $y=0.3 x^{3}$ , the $x-$ axis, and $x=3$

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Problem 1507

2. Find the domain of the function $f(x)=\frac{x^{2}-1}{x^{2}-9}$ .
Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. The domain is $\{x \mid$ $\qquad$ \}. (Simplify your answer. Type an inequality. Use a comma to separate answers as needed.) B. The domain is $\{x \mid x \neq$ $\qquad$ 3. (Simplify your answer. Use a comma to separate answers as needed.) C. The domain is $\{x \mid x \leq$ $\qquad$ , $x \neq$ $\qquad$ \}. (Simplify your answer. Use a comma to separate answers as needed.) D. The domain is $\{x \mid x \geq$ $\qquad$ , $x \neq$ $\qquad$ \}. (Simplify your answer. Use a comma to separate answers as needed.) E. The domain is the set of all real numbers.

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Problem 1508

Determine the signs (positive, negative, or zero) of $y=f(x)$ (shown in the graph), $f^{\prime}(x)$ , and $f^{\prime \prime}(x)$ when $x=1$ .
The sign of $f(1)$ is Select an answer $v$ The sign of $f^{\prime}(1)$ is Select an answer $\vee$ The sign of $f^{\prime \prime}(1)$ is Select an answer $v$

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Problem 1509

Find $f^{\prime}(x)$ . $\begin{array}{l} f(x)=\left(5 x^{6}+6\right)^{3} \\ f^{\prime}(x)=\square \end{array}$

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Problem 1510

Differentiate. $\begin{array}{c} y=\ln \left[(x+6)^{3}(x+7)^{6}(x+2)^{4}\right] \\ \frac{d}{d x}\left[\ln \left[(x+6)^{3}(x+7)^{6}(x+2)^{4}\right]\right]= \end{array}$

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Problem 1511

Differentiate the following function. $\begin{array}{l} y=(\ln x)^{8}+\ln \left(x^{8}\right) \\ \frac{d y}{d x}=\square \end{array}$ $\square$

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Problem 1512

Given the function $g(x)=6 x^{3}+18 x^{2}-144 x$ , find the first derivative, $g^{\prime}(x)$ . $g^{\prime}(x)=$ $\square$ Notice that $g^{\prime}(x)=0$ when $x=-4$ , that is, $g^{\prime}(-4)=0$ . Now, we want to know whether there is a local minimum or local maximum at $x=-4$ , so we will use the second derivative test. Find the second derivative, $g^{\prime \prime}(x)$ . $g^{\prime \prime}(x)=$ $\square$ Evaluate $g^{\prime \prime}(-4)$ . $g^{\prime \prime}(-4)=$ $\square$ Based on the sign of this number, does this mean the graph of $g(x)$ is concave up or concave down at $x=-4$ ? At $x=-4$ the graph of $g(x)$ is Select an answer $v$ Based on the concavity of $g(x)$ at $x=-4$ , does this mean that there is a local minimum or local maximum at $x=-4$ ? At $x=-4$ there is a local Select an answer $\checkmark$

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Problem 1513

$\mathrm{t}=18$ days? Answer in appropriate units.

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Problem 1514

Evaluation \& Substitution
The marginal cost (dollars) of printing a poster when $x$ posters have been printed is $\frac{d c}{d x}=\frac{1}{\sqrt[5]{x^{4}}}$ . Find $c(160)-c(13)$ , the cost of printing posters 14 through 160 .
The cost of printing posters 14 through 160 is $\$$ $\square$ (Round to the nearest cent.)

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Problem 1515

2. Let $S(t)=\frac{1}{1+e^{-t}}$ . a. Find $S^{\prime}(t)$ . Show your work completely to justify your response. b. Which of the following equations hold true? Explain your thinking fully. (Note: Only one equation is true.) 1) $S^{\prime}(t)=S(t)$ 2) $S^{\prime}(t)=(S(f))^{2}$ 3) $S^{\prime}(t)=S(t)(1-S(t))$ 4) $S^{\prime}(t)=-S(-t)$
Note: The function $S(f)$ is called the "Sigmoid activation function" and is extremely important in machine learning and artificial intelligence.

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Problem 1516

Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the x -axis or touches the x-axis and turns around at each zero. $f(x)=x^{3}+3 x^{2}-4 x-12$
Determine the zero(s), if they exist. The zero(s) is/are $\square$ . (Type integers or decimals. Use a comma to separate answers as needed.)

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Problem 1517

5. [-/1 Points]
DETAILS MY NOTES TANAPCALC10 6.5.0 Find the average value of the function $f$ over the interval $[4,9]$ . $f(x)=7-x$ $\square$

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Problem 1518

$1 \leftarrow \quad$ Find $\frac{d y}{d x}$ $\begin{array}{l} y=\int_{x}^{1} \sqrt{t^{4}+5} d t \\ \frac{d y}{d x}=\square \end{array}$ $\square$

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Problem 1519

\begin{align} \text{(c)} & \quad f(\sqrt{177}) \approx \square \\ \text{Part 4 of 6} \\ \text{(d)} & \quad f(4 \pi) \approx \square \\ \text{Part 5 of 6} \\ \text{(e)} & \quad f\left(6.5 \times 10^{7}\right) \approx \square \\ \end{align}
\text{Approximate } f(x) = \ln x \text{ for the given values of } x. \text{ Round to 4 decimal places.}

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Problem 1520

Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around at each zero. $f(x)=x^{3}+3 x^{2}-4 x-12$
Determine the multiplicities of the zero(s), if they exist. Select the correct choice below and, if necessary, fill in the answer box(es) within your choice. A. There is one zero. The multiplicity of the zero is $\square$ I. (Simplify your answer.) B. There are three zeros. The multiplicity of the smallest zero is 1. . The multiplicity of the largest zero is $\hat{1}$ . The multiplicity of the other zero is 1 . (Simplify your answers.), C. There are two zeros. The multiplicity of the smallest zero is $\square$ . The multiplicity of the largest zero is $\square$ . (Simplify your answers.) Determine the behavior of the function at each zero. Select the correct choice below and, if necessary, fill in the answer boxes within your choice. A. The graph crosses the $x$ -axis at $x=$ $\square$ . The graph touches the $x$ -axis and turns around at $x=$ $\square$ . (Type integers or decimals. Simplify your answers. Use a comma to separate answers as needed.) B. The graph touches the $x$ -axis and turns around at all zeros. C. The graph crosses the $x$ -axis at all zeros. Get more help - Clear all Skill builder Check answe

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Problem 1521

ㅇ webassign.net/web/Student/Assignment-Responses/submit?dep=34800833\&tags=autosave\#question3716073_6
7. [0/1 Points]
DETAILS MY NOTES TANAPCALC10 6.5.051. PREVIOUS ANSWERS PRACTICE ANOTHER Cell Phone Ad Spending A certain industry's ad spending between $2005(t=1)$ and $2011(t=7)$ is projected to be $S(t)=0.88 t^{0.94} \quad(1 \leq t \leq 7)$ where $S(t)$ is measured in billions of dollars and $t$ is measured in years. What is the projected average spending per year on these ads between 2005 and 2011 ? (Round your answer to two decimal places.)

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Problem 1522

Calculate the left and right Riemann sums.

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Problem 1523

Use Descartes's Rule of Signs to determine the possible numbers of positive and negative real zeros of $f(x)=9 x^{4}-7 x^{3}-4 x^{2}-6 x+7$ .
What is the possible number of positive real zeros? $\square$ (Use a comma to separate answers as needed.)

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Problem 1524

For the high school basketball game, it costs $\$ 8$ for every 4 tickets. Complete the table below showing the cost and the number of tickets. \begin{tabular}{|l|c|c|c|c|c|} \hline Cost (\) & \square & 8 & 14 & \square & 20 \\ \hline Number of tickets & 1 & 4 & \square & 9 & \square$ \\ \hline \end{tabular}

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Problem 1525

(1 point)
Differentiate $y=\sqrt{1-x^{2}} \sin ^{-1} x$ $y^{\prime}=$

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Problem 1526

Figure 1
Figure 2
Figure 3 (a) Which curve fits the data best? Figure 1 Figure 2 Figure 3 (b) Use the equation of the best fitting curve from part (a) to predict the speed of the object at 8 seconds. Give an exact answer, not a rounded approximation. $\square$ meters per second

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Problem 1527

Find $f^{\prime}$ , given $f^{\prime}(x)=1, f(x)=\frac{x \sin ^{3}\left(x^{2}\right)}{\sqrt{x^{5}+1}}$

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Problem 1528

A printer is printing photos. For every 20 photos, the printer takes 4 minutes. Complete the table below showing the number of photos and the time it takes to print them. \begin{tabular}{|l|c|c|c|c|c|} \hline Number of photos & 20 & $\square$ & $\square$ & 45 & $\square$ \\ \hline Time (minutes) & 4 & 5 & 7 & $\square$ & 10 \\ \hline \end{tabular}

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Problem 1529

7. [-/1 Points] DETAILS MY NOTES SESSCALCET2 7.2.029.
A CAT scan produces equally spaced cross-sectional views of a human organ that provide information about the organ otherwise obtained only by surgery. Suppose that a CAT scan of a human liver shows cross-sections spaced 1.5 cm apart. The liver is 15 cm long and the cross-sectional areas, in square centimeters, are $0,17,58,79,93,107,116,128,63,38$ , and 0 . Use the Midpoint Rule with $n=5$ to estimate the volume $V$ of the liver. $v=$ $\qquad$ $\mathrm{cm}^{3}$ Need Help? Watch 17 Submil Answer

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Problem 1530

30. A rock is thrown upward from the edge of a bridge and onto a road that is 10 feet below the bridge. The function $h(x)=-x^{2}+3 x+10$ gives the height, $h$ , in feet, the rock travels in $x$ seconds from the time it was thrown. When will the rock hit the road?
31. Write an equation of a parabola with $x$ -intercepts at $\left(\frac{1}{4}, 0\right)$ and $(-7,0)$ which passes through the point $(0,7)$ .
Use square roots to solve each equation. Write your solutions using the imaginary unit, $i$ .
32. $x^{2}=-81$
33. $x^{2}=-625$
34. $x^{2}=-144$
Simplify each expression.
35. $(-2+3 i)+(5-2 i)$
36. $(-6+7 i)+(6-7 i)$ $37 .(8+5 i)+(6-7 i)$

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Problem 1531

the functions $f(x)=\frac{2}{x+3}$ and $g(x)=\frac{11}{x+2}$ , find the compositio tation. $(f \circ g)(x)=$ $\square$
Domain of $f \circ g$ : $\square$

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Problem 1532

Find the general antiderivative, $F(x)$ , of the function $f(x)=\frac{4}{5} x^{9}-\frac{9}{10} x^{10}+x^{7}$ $F(x)=$

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Problem 1533

where $C$ is an arbitrary constant.
Find the general antiderivative, $F(x)$ , of the function $f(x)=-\frac{6 \sqrt[2]{x^{7}}}{4}-\frac{6 x^{10}}{7}+8$ $F(x)=$ $\square$

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Problem 1534

Find the general antiderivative, $F(x)$ , of the function $f(x)=\frac{2}{x^{4}}-6-\frac{4}{x^{5}}$ $F(x)=$

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Problem 1535

Determine the signs (positive, negative, or zero) of $y=f(x)$ (shown in the graph), $f^{\prime}(x)$ , and $f^{\prime \prime}(x)$ when $x=1$ .
The sign of $f(1)$ is Select an answer $\vee$ The sign of $f^{\prime}(1)$ is Select an answer $\checkmark$ The sign of $f^{\prime \prime}(1)$ is Select an answer $\vee$

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Problem 1536

$\begin{array}{l}f(x)=\left\{\begin{array}{ll}x+2 & 4<x<5 \\ x+3 & 5 \leqslant x<6\end{array}\right. \\ f(5)=\end{array}$

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Problem 1537

3. Each side of a square is increasing at a rate of $6 \mathrm{~cm} / \mathrm{s}$ . At what rate is the area of the square increasing when the area of the square is $16 \mathrm{~cm}^{2}$ ?

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Problem 1538

9 Mark for Review 40
The function $f$ is defined by $f(x)=x^{2} e^{-x^{2}}$ . At what values of $x$ does $f$ have a relative maximum? (A) -2 (B) 0 (C) 1 only (D) -1 and 1

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Problem 1539

DEL - Ap pre-calc: Calculator licbits
Instructions: For each function, find all (1) $G(x)=(x-1)^{2}$
Zeroes: -1.41 \ $1.41 Reli Max: None Reli min: -2$ F(1.2):-.56 $(2)$ A(x)=-\frac{(x+5)^{3}}{4}$
Zeroes: Relimax Reli min: $f(1.2)$ : (3) $R(x)=x^{4}-x^{3}-4 x^{2}+1$
Zeroes: Reli Max: Reli Min: $F(1.2)$ : (4) $6(x)=\frac{6 x^{2}+2 x-1}{x^{2}-9}-10$ zeroes: Reli Max: Reli Min: $f(12):$

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Problem 1540

Sketch three different quartic functions which contain the given points: $(-7,0) ;(-4,0) ;(0,5) ;(3,0)$

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Problem 1541

Consider the function $f(x)=5 x+5 x^{-1}$ . For this function there are four important intervals: $(-\infty, A],[A, B),(B, C]$ , and $[C, \infty)$ where $A$ , and $C$ are the critical numbers and the function is not defined at $B$ . Find $A$ $\square$ and $B$ $\square$ and $C$ $\square$ For each of the following open intervals, tell whether $f(x)$ is increasing or decreasing. $(-\infty, A)$ : Select an answer $\checkmark$ $(A, B)$ : Select an answer $(B, C)$ : Select an answer $(C, \infty)$ Select an answer $\vee$ Note that this function has no inflection points, but we can still consider its concavity. For each of the following intervals, tell whether $f(x)$ is concave up or concave down. $(-\infty, B):$ Select an answer $\vee$ $(B, \infty)$ : Select an answer $\vee$

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Problem 1542

Evaluate the following expression without using a calculator. $\log _{6}(\sqrt{6})$

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Problem 1543

30. For the two functions $y=-2(x+5)^{2}+q$ and $y=2(x+5)^{2}-q, q>0$ , How many times do they intersect?

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Problem 1544

14. $f(x)=3 x^{3}+8 x^{2}+3 x-2 ;(x+2)$
16. $f(x)=8 x^{4}-24 x^{3}-x+3 ;(x-3)$

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Problem 1545

Question On the graph below, move the two points to graph the oblique asymptote for the function $f(x)=\frac{-x^{2}-x+1}{x-1}$
Provide your answer below: FEEDBACK MORE INSTRUCTION SUBMIT Content attribution

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Problem 1546

What is the range of the sine function?
The range of the sine function is $\square$ (Type your answer in interval notation.)

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Problem 1547

Biology Because of an insufficient oxygen supply, the trout population in a lake is dying. The population's rate of change can be modeled by $\frac{d p}{d t}=-115 e^{-t / 30}$ where $t$ is the time in days. When $t=0$ , the population is 3,450 . (a) Find a model for the population. $P(t)=3450 e^{-\left(\frac{t}{30}\right)}$ (b) What is the population of fish after 19 days? (Round your answer to the nearest integer.)
1893 $\qquad$ fish $\square$ days

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Problem 1548

Solve a Specific Antiderivative (aka Initial Value) Problem.
The marginal cost function for Mark Hall's Bulk Greeting Cards is given by $C^{\prime}(x)=\frac{8}{\sqrt{x}}$ dollars per box when $x$ boxes of greeting cards are sold. If the cost of making and shipping 49 boxes of cards is $\$ 226$ , find the company's cost function, in dollars, when $x$ boxes of greeting cards are sold. $C(x)=$ $\square$ dollars per week.

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Problem 1549

4 Mark for Review APS
Which of the following functions of $x$ is guaranteed by the Extreme Value Theorem to have an absolute maximum on the interval $[0,2 \pi]$ ? (A) $y=\frac{1}{1+\sin x}$ (B) $y=\frac{1}{x^{2}+\pi}$ (C) $y=\frac{x^{2}-2 \pi x+\pi^{2}}{x-\pi}$ (D) $y=\frac{|x-\pi|}{x-\pi}$

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Problem 1550

8. Find $(g+h)(x)$ if * 7 points $\begin{array}{l} g(x)=2 x^{3}+3 x-4 \\ h(x)=2 x^{2}-x+3 \end{array}$ $4 x^{3}+2 x-1 \quad 4 x^{5}+2 x-1$ A B $2 x^{3}+2 x^{2}+2 x-1 \quad 8 x^{6}-1$

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Problem 1551

1. Identify the parent function. Then describe the transformations that produce the graph of $f$ . a. $f(x)=|x+9|$ b. $f(x)=5 x^{3}-8$

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Problem 1552

The population in a certain city was 57,000 in 2000 , and its future size is predicted to be $\mathrm{P}(\mathrm{t})=57,000 e^{0.018 t}$ , where t is the number of years after 2000.
Complete parts a through d below. a. Does this model indicate that the population is increasing or decreasing? increasing decreasing b. Use this function to estimate the population of the city in 2009. $\square$ (Round to the nearest whole number as needed.)

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Problem 1553

10. Find $(h-g)(x)$ * 6 points $\begin{array}{l} g(x)=3 x+1 \\ h(x)=x^{3}-2 \end{array}$ $2 x^{4}-1$ $2 x^{4}+3$ Option 1 Option 2 $-x^{3}+3 x+3$ $-x^{3}+3 x-1$

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Problem 1554

8. [-/1 Points] DETAILS MẎ NOTES
Find a formula for the inverse of the given function. $\begin{array}{c} f(x)=x^{6} \\ y=\square \end{array}$ Need Help? Read It

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Problem 1555

Find the derivative of the function $f(x) = 4x e^{2x}$ , and then find the critical points of the function.

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Problem 1556

6 Mark for Review AP
The function $f$ is defined by $f(x)=e^{-x}\left(x^{2}+2 x\right)$ . At what values of $x$ does $f$ have a relative maximum?
A $x=-2+\sqrt{2}$ and $x=-2-\sqrt{2}$
B $x=-\sqrt{2}$ only (C) $x=-2$ and $x=0$ (D) $x=\sqrt{2}$ only

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Problem 1557

3. Using the graph of $g(x)$ shown, sketch the transformation $g(-x)+2$ on the same coordinate grid.

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Problem 1558

7 ■ Mark for Review
Let $f$ be a differentiable function with a domain of $(0,10)$ . It is known that $f^{\prime}(x)$ , the derivative of $f(x)$ , is negative on the intervals $(0,2)$ and $(4,6)$ and positive on the intervals $(2,4)$ and $(6,10)$ . Which of the following statements is true? A) $f$ has no relative minima and three relative maxima. (B) $f$ has one relative minimum and two relative maxima. (C) $f$ has two relative minima and one relative maximum.
D $f$ has three relative minima and no relative maxima.

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Problem 1559

4. Submit answer Practice similar
Find the area bounded by the curves $y=e^{x}+1$ and $y=3 x$ over the interval $[0,1]$ . (Round your answer to two decimal places.) $\square$ Video Example: Solving A Similar Problem

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Problem 1560

8 Mark for Review
Let $f$ be the function with derivative $f^{\prime}(x)=x^{3}-3 x-2$ . Which of the following statements is true?
A $f$ has no relative minima and one relative maximum. (B) $f$ has one relative minimum and no relative maxima. (C) $f$ has one relative minimum and one relative maximum. (D) $f$ has two relative minima and one relative maximum.

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Problem 1561

www-awu.aleks.com Untitled document - Traditional | Stats | N... Defense | Stats | NBA... Utah vs LA Stats \& P... Ivica Zubac /II Stats /... Home - Northern Ess.. Content Midterm Exam: Ch $1(1,2) 2(1,2,3) 3(1,2,3) 4(1,2) 5(1,2,3) 6(1,2)$ Question 19 of 30 (1 point) I Question Attempt: 1 of 1 Time Remaining: 1:06:58 Jonathan 13 $=14$ $\equiv 15$ 16 17 18 19 20 21 22 23 24
The following table presents the percentage of students who tested proficient in reading and the percentage who tested proficient in math for 5 randomly selected states in the United States. Compute the least-squares regression line for predicting math proficiency from reading proficiency. \begin{tabular}{|l|c|c|} \hline \multicolumn{1}{|c|}{ State } & \begin{tabular}{c} Percent Proficient \\ in Reading \end{tabular} & \begin{tabular}{c} Percent Proficient \\ in Mathematics \end{tabular} \\ \hline Illinois & 75 & 70 \\ \hline Texas & 73 & 78 \\ \hline Ohio & 79 & 76 \\ \hline New York & 75 & 70 \\ \hline Georgia & 67 & 64 \\ \hline \end{tabular}
Send data to Excel
The equation for the least squares regression line is $\hat{y}=$ $\square$ . Round the slope and $y$ -intercept to four decimal places as needed.

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Problem 1562

homework5.1: Problem 2 (1 point)
For time, $t$ , in hours, $0 \leq t \leq 1$ , a bug is crawling at a velocity, $v$ , in meters/hour given by $v=\frac{2}{2+t}$
Use $\Delta t=0.2$ to estimate the distance that the bug crawls during this hour. Use left-and right-hand Riemann sums to find an overestimate and an underestimate. Then average the two to get a new estimate. underestimate $=$ $\square$ overestimate $=$ $\square$ average = $\square$ (for each, include help (units)
Note: You can earn partial credit on this problem.

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Problem 1563

2. Let $f(x)=x^{3}+5 x$ . Is $f$ even, odd, or neither? Prove your answer algebraically.

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Problem 1564

3. Ben was asked to determine if the function $f(x)=x^{3}-4 x^{2}-4 x+19$ was even, odd, or neither. His work is shown below. $\begin{array}{l} f(2)=2^{3}-4\left(2^{2}\right)-4(2)+19=3 \\ f(-2)=(-2)^{3}-4(-2)^{2}-4(-2)+19=3 \end{array}$
Because $f(2)=f(-2), f(x)$ is even. Imagine you were Ben's teacher. What feedback would you give him?

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Problem 1565

14 Mark for Review Aps \begin{tabular}{|l|l|l|l|} \hline & & & \\ \hline & & & \\ \hline & & & \\ \hline $x$ & & & \\ \hline \end{tabular}
The figure above represents a square sheet of cardboard with side length 20 inches. The sheet is cut and pieces are discarded. When the cardboard is folded, it becomes a rectangular box with a lid. The pattern for the rectangular box with a lid is shaded in the figure. Four squares with side length $x$ and two rectangular regions are discarded from the cardboard. Which of the following statements is true? (The volume $V$ of a rectangular box is given by $V=l w h$ .) (A) When $x=10$ inches, the box has a minimum possible volume.
B When $x=10$ inches, the box has a maximum possible volume. C) When $x=\frac{10}{3}$ inches, the box has a minimum possible volume.
D When $x=\frac{10}{3}$ inches, the box has a maximum possible volume.

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Problem 1566

Identify the vertex of the parabola: $\square$ Remember that the vertex is a point! Identify the $y$ -intercept of the parabola: $\square$ Remember that the $y$ -intercept is a point! Identify the $x$ -intercepts: $\square$ and $\square$ Remember tllat the $x$ -intercepts represent points on the graph! Given the $x$ -intercepts above, write an equation for the parabola in factored for $y=$ $\square$ Hint: Think about the zero-product property. Write an equation for the axis of symmetry: $\square$

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Problem 1567

15 Mark for Review $4 \%$ \begin{tabular}{|c||c|c|c|c|} \hline $x$ & 0 & 1 & 2 & 3 \\ \hline $f(x)$ & 15 & 14 & 12 & 9 \\ \hline \end{tabular}
Let $f$ be a function with selected values given in the table above. Which of the following statements must be true? I. By the Intermediate Value Theorem, there is a value $c$ in the interval $(0,3)$ such that $f(c)=10$ . II. By the Mean Value Theorem, there is a value $c$ in the interval $(0,3)$ such that $f^{\prime}(c)=-2$ . III. By the Extreme Value Theorem, there is a value $c$ in the interval $[0,3]$ such that $f(c) \leq f(x)$ for all $x$ in the interval $[0,3]$ . (A) None (B) Ionly (C) 11 only (D) $1, I I$ , and III

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Problem 1568

Suppose that $\$ 18,804$ is invested at an interest rate of $6.5 \%$ per year, compounded continuously. a) Find the exponential function that describes the amount in the account after time $t$ , in years. b) What is the balance after 1 year? 2 years? 5 years? 10 years? c) What is the doubling time? a) The exponential growth function is $\mathrm{P}(\mathrm{t})=18,804 \cdot e$ . (Type exponential notation with positive exponents. Do not simplify. Use integers or decimals for any numbers in the equation.)

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Problem 1569

Evaluate the function at the specified points. $f(x, y)=y+x y^{2},(-2,4),(-3,-2),(-5,4)$
At $(-2,4)$ : $\square$ At $(-3,-2)$ : $\square$ At $(-5,4)$ : $\square$ Submit answer Next item

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Problem 1570

Find the derivative of the function. $\begin{array}{l} h(t)=11 \cot ^{-1}(t)+11 \cot ^{-1}\left(\frac{1}{t}\right) \\ h^{\prime}(t)=\square \end{array}$

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Problem 1571

17 Mark for Review Aps.
Let $f$ be a twice-differentiable function. Which of the following statements are individually sufficient to conclude that $x=2$ is the location of the absolute maximum of $f$ on the interval $[-5,5]$ ? I. $f^{\prime}(2)=0$ II. $x=2$ is the only critical point of $f$ on the interval $[-5,5]$ , and $f^{\prime \prime}(2)<0$ . III. $x=2$ is the only critical point of $f$ on the interval $[-5,5]$ , and $f(-5)<f(5)<f(2)$ . (A) II only (B) Ill only (C) I and II only
D DI and III only

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Problem 1572

[-/0.5 Points] DETAILS MY NOTES TANAPMATH7 10.2.058.
Find the inflection point(s), if any, of the function. (If an answer does not exist, enter DNE.) $g(x)=4 x^{4}-8 x^{3}+6$ smaller $x$ -value $(x, y)=$ $\square$ ) larger $x$ -value $(x, y)=$ $\square$ ) Need Help? Read it

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Problem 1573

Find a formula for the inverse of the following function, if possible. $s(x)=\sqrt[3]{4 x-5}$
Answer How to enter your answer (opens in new window)
Selecting a radio button will replace the entered answer value(s) with the radio button value. If the radio button is not selected, the entered answer is used. $s^{-1}(x)=$ does not have an inverse function

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Problem 1574

2. Let $f(x)=\sqrt{20-x}$ and $g(x)=\sqrt{10 x-4}$ . Let $h(x)=f(x) g(x)$ . Find $h(4)$ .

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Problem 1575

Use difference quotients with $\Delta x=0.1$ and $\Delta y=0.1$ to estimate $f_{x}(4,2)$ and $f_{y}(4,2)$ where $f(x, y)=e^{-x} \sin (y) .$ $\begin{array}{l} f_{x}(4,2) \approx \\ f_{y}(4,2) \approx \end{array}$ $\square$ $\square$ Then give better estimates by using $\Delta x=0.01$ and $\Delta y=0.01$ . $\begin{array}{l} f_{x}(4,2) \approx \square \\ f_{y}(4,2) \approx \square \end{array}$ Submit answer Next item

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Problem 1576

Follow the steps for graphing a rational function to graph the function $R(x)=\frac{x+3}{x(x+9)}$ .
Determine the behavior of the graph of R at any x -intercepts. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. The graph will cross the $x$ -axis at $x=$ $\square$ and touch but not cross the $x$ -axis at $x=$ $\square$ . (Type integers or simplified fractions. Use a comma to separate answers as needed. Type each answer only once.) B. The graph will touch but not cross the $x$ -axis at $x=$ $\square$ (Type integers or simplified fractions. Use a comma to separate answers as needed Type each answer only once.) C. The graph will cross the $x$ -axis at $x=$ $\square$ . (Type integers or simplified.fractions. Use a comma to separate answers as needed. Type each answer only once.) D. The function has no $x$ -intercept.
Determine the vertical asymptote(s), if one exists. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. The function has three vertical asymptotes. The leftmost asymptote is $\square$ , the middle asymptote is $\square$ , and the rightmost asymptote is $\square$ . (Type equations. Use integers or fractions for any numbers in the equations.) B. The function has two vertical asymptotes. The leftmost asymptote is $\square$ , and the rightmost asymptote is $\square$ . (Type equations. Use integers or fractions for any numbers in the equations.) C. The function has one vertical asymptote, $\square$ . (Type an equation. Use integers or fractions for any numbers in the equation.) D. The function has no vertical asymptote.

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Problem 1577

$\begin{array}{l}\lim _{x \rightarrow 1} f(x) \\ f(x)=\left\{\begin{array}{ll}x^{2}+3, & x \neq 1 \\ 2, & x=1\end{array}\right.\end{array}$

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Problem 1578

18 Mark for Review \begin{tabular}{|c|c|c|c|c|c|c|} \hline $x$ & 0 & 2 & 4 & 6 & 8 & 10 \\ \hline $f^{\prime}(x)$ & -1 & 0 & -2 & 3 & 0 & -1 \\ \hline $f^{\prime \prime}(x)$ & 8.333 & -1.900 & 0.971 & -0.304 & 0.400 & -4.167 \\ \hline \end{tabular}
Let $f$ be a twice-differentiable function. Selected values of $f^{\prime}$ and $f^{\prime \prime}$ are shown in the table above. Which of the following statements are true? I. $f$ has neither a relative minimum nor a relative maximum at $x=2$ . II. $f$ has a relative maximum $x=2$ . III. $f$ has a relative maximum $x=8$ . (A) Ionly (B) II only (C) III only (D) I and III only

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Problem 1579

Use the Remainder Theorem to evaluate each polynomial for the given value of $x$ . SEE EXAMPLE 4
24. $f(x)=x^{3}+9 x^{2}+3 x-7 ; x=-5$
25. $f(x)=2 x^{3}-3 x^{2}+4 x+13 ; x=3$
26. $f(x)=-x^{4}+2 x^{3}-x^{2}+4 x+8 ; x=-2$
27. $f(x)=x^{5}-3 x^{4}-2 x^{3}+x^{2}-2 x-1 ; x=4$

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Problem 1580

Find $d y / d x$ using the method of logarithmic differehtiation when $y=x^{4 \cos (x)}$ . $d y / d x=4 x^{\wedge}(4 \cos x)(\operatorname{co}$

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Problem 1581

Let $f$ be the function defined by $f(x)=3 x^{2}-x^{3}$ . What is the absolute minimum value of $f$ on the closed interval $\left[1, \frac{5}{2}\right]$ ? (A) 0 (B) 2 (C) $\frac{25}{8}$ (D) 4

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Problem 1582

20 Mark for Review
Let $g$ be the function given by $g(x)=3 x^{4}-8 x^{3}$ . At what value of $x$ on the closed interval $[-2,2]$ does $g$ have an absolute maximum? (A) -2 (B) 0 (C) 2 (D) $\frac{8}{3}$

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Problem 1583

21 Mark for Review 420
Let $f$ be the function defined by $f(x)=12 x-x^{3}$ . What is the absolute minimum value of $f$ on the closed interval $[0,3]$ ? (A) -16 (B) 0 (C) 9 (D) 16

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Problem 1584

Let $\begin{array}{l} f(x)=\frac{x}{\cos x^{3}} . \\ f^{\prime}(x)=\square \end{array}$

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Problem 1585

Which is the first transformation that should be applied to transform the parent function $f(x)=\log _{10} x$ to graph the transformed function $f(x)=4 \log _{10}(x-5)+3$ ? a. Vertical stretch by a factor of 4 b Horizontal translation 5 units to the right c. Vertical translation 3 units up d. Vertical compression by a factor of 4

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Problem 1586

28 Mark for Review
The first derivative of the function $h$ is given by $h^{\prime}(x)=x^{4}-x^{3}+x$ . On which of the following intervals is the graph of $h$ concave down? (A) $(-0.755,0)$ (B) $(0,0.5)$ only (C) $(-0.455, \infty)$ (D) $(-\infty,-0.455)$

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Problem 1587

29 Mark for Review Auto saved at: 21 :40:44
The first derivative of the function $h$ is given by $h^{\prime}(x)=x^{5}-3 x^{2}+x$ . What are all intervals on which the graph of $h$ is concave down? (A) $(-\infty, 0)$ and $(0.338,1.307)$ (B) $(-\infty, 0.669)$ (C) $(-\infty, 0.167)$ and $(1, \infty)$ (D) $(0.167,1)$

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Problem 1588

A sink is filled with 54 quarts of water. The function $q=f(t)=54-2.5 t$ gives the volume of wate in the sink, in quarts, $t$ seconds after removing the stopper. a. Find $f^{-1}$ . b. What does the input of $f^{-1}$ represent? What does the output of $f^{-1}$ represent? c. How long will it take for the sink to drain completely? d. How long will it take for the sink to lose one-third of its water?

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Problem 1589

Warrensville Heights City Schoc DeltaMath Student Application Dej Loaf - Fools Fall...
Question Watchivides
Lydia was given a box of assorted chocolates for her birthday. Each night, Lydia treats herself to some chocolates. Let $C$ represent the number of choo remaining in the box $t$ days after Lydia's birthday. A graph of $C$ is shown below. Write an equation for $C$ then state the $x$ -intercept of the graph and o interpretation in the context of the problem. $C=$ $\square$ The $x$ -intercept of the function is $\square$ which represents $\square$ Bumit Aarwy

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Problem 1590

$31 \square$ Mark for Review Let $f$ be the function with derivative given by $f^{\prime}(x)=\sin x+\cos (2 x)-\frac{\pi}{4}$ for $0 \leq x \leq \pi$ . On which of the following intervals is $f$ increasing? (A) $[0,0,724]$ only (B) $[0,0.724]$ and $[2.418,3.142]$ (C) $[0,0.253]$ and $[1.571,2.889]$ (D) $[0.724,2.418]$

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Problem 1591

What are the vertical asymptotes of the graph of $f$ ?
The vertical asymptote(s) is/are $\square$ $\square$ . (Type an equation. Use a comma to separate answers as needed.)

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Problem 1592

3. When a song is sold by an online mustc store, the store takes some of the money, and the stiger gests the
10. rest. The graph below shows how much money a pop singer makes given the total amount of money brought in by one popular online music store from sales of the song. a. Identify the constant of proportionality between dollars earned by the pop singer and dollars brought in by sales of the song.

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Problem 1593

32 Mark for Review
Let $f$ be the function with derivative given by $f^{\prime}(x)=\sin x+x \cos x$ for $0<x \leq \pi$ . On which of the following intervals is $f$ increasing? (A) $[0,1.077]$ only (B) $[0,2.029]$ (C) (D) $[2.029, \pi]$ only

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Problem 1594

Consider the function $B(t)$ that gives the temperature of Boston, Massachusetts on a particular day, where $t$ is measured in hours after midnight. Is $B(t)$ a one-to-one function? How do you know?

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Problem 1595

Use the change-of-base formula and a calculator to approximate the given logarithm. Round to 4 decimal places. Then check the answer by using the related exponential form. $\log _{4}\left(2.97 \times 10^{-4}\right)$
Part: $0 / 2$
Part 1 of 2
Approximate the logarithm to 4 decimal places. If necessary, round intermediate steps to 9 decimal places. $\log _{4}\left(2.97 \times 10^{-4}\right) \approx \square$

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Problem 1596

Submit Answer
14. [0.38/0.5 Points]
DETAILS MY NOTES
TANAPMATH7 10.1.029.EP. PREVIOUS ANSWERS
Consider the following function. $g(t)=\frac{9 t}{t^{2}+4}$
Find the derivative of the function. $g^{\prime}(t)=\frac{-9 t^{2}+36}{\left(t^{2}+4\right)^{2}} \quad$ Nice job. Find all the values of $t$ for which $g^{\prime}(t)=0$ or $g^{\prime}(t)$ is discontinuous. (Enter your answers as a comma-separated list.) $t=$ $\square$ Please remove the grouping symbols from around your list. Find the interval(s) where the function is increasing and the interval(s) where it is decreasing. (Enter your answers using interval notation. If the answer cannot be expressed as an interval increasing $\quad(-2,2)$ Terrific! decreasing $(-\infty,-2) \cup(2, \infty)$ - Good job. Need Help? Read II

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Problem 1597

1. The function $f$ defined by $y=f(x)=-x^{2}+6 x-5$ has (A) A minimum $y$ value and a negative $y$ -intercept. (B) A maximum $y$ value and a positive $y$ -intercept. (C) A minimum $y$ value and a positive $y$ -intercept. (D) A maximum $y$ value and a negative $y$ -intercept.

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Problem 1598

7. Write an equation for a function that is the reciprocal of a quadratic and has the following properties: - The horizontal asymptote is $y=0$ . - The vertical asymptotes are $x=-4$ and $x=5$ . - For the intervals $x<-4$ and $x>5, y<0$ .

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Problem 1599

Graph the polynomial function $f(x)=x^{2}(x-4)$ using parts (a) through (e). (a) Determine the end behavior of the graph of the function.
The graph of $f$ behaves like $y=x^{3}$ for large values of $|x|$ . (b) Find the $x$ - and $y$ -intercepts of the graph of the function.
The $x$ -intercept(s) is/are 0,4. (Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed. Type each answer only once.)
The $y$ -intercept is 0 . (Simplify your answer. Type an integer or a fraction.) (c) Determine the zeros of the function and their multiplicity. Use this information to determine whether the graph crosses or touches the x-axis at each x-intercept. The zero(s) of f is/are 0,4 . (Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed. Type each answer only once.)
The lesser zero of the function is of multiplicity $\square$ , so the graph of $f$ crosses the $x$ -axis at $\mathrm{x}=$ $\square$ . The greater zero of the function is of multiplicity at $x=$ $\square$ $\square$ , so the graph of $f$ touches the $x$ -axis

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Problem 1600

2. The cost, $C$ , in dollars, of shipping a package that weighs $w$ pounds can be modeled by the function given by $C(w)=\left\{\begin{array}{ll} 11 & 0<w<2 \\ 9+1.49 w & 2 \leq w<10 \\ 6+1.99 w & w \geq 10 \end{array}\right.$ a. How much does it cost to ship a package that weighs 1.5 pounds? b. How much does it cost to ship a package that weighs 5 pounds? c. How much more does it cost to ship a package that weighs 10 pounds than a package that weighs 9 pounds?

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Function

Problem 1501

The function f(x)=9x+7x−1f(x)=9 x+7 x^{-1}f(x)=9x+7x−1 has one local minimum and one local maximum. This function has a local maximum at x=x=x= □\square□ with value □\square□ and a local minimum at x=x=x= □\square□ with value □\square□

Problem 1502

Problem 1503

Question 7An exponential function f(x)=a⋅bxf(x)=a \cdot b^{x}f(x)=a⋅bx passes through the points (0,7000)(0,7000)(0,7000) and (3,56)(3,56)(3,56). What are the values of aaa and bbb ? a=a=a= □\square□ and b=b=b= □\square□

Problem 1504

Problem 1505

Period: DUE: Tuesdav, 11/19/241. Find the volume of the solid obtained by rotating the region given about the x -axis and using the given bounds. Sketch a picture of the graph. y=0.3x3y=0.3 x^{3}y=0.3x3, the x−x-x− axis, and x=3x=3x=3

Problem 1506

Period: DUE: Tuesdav, 11/19/241. Find the volume of the solid obtained by rotating the region given about the x -axis and using the given bounds. Sketch a picture of the graph. y=0.3x3y=0.3 x^{3}y=0.3x3, the x−x-x− axis, and x=3x=3x=3

Problem 1507

Problem 1508

Problem 1509

Find f′(x)f^{\prime}(x)f′(x). f(x)=(5x6+6)3f′(x)=□\begin{array}{l} f(x)=\left(5 x^{6}+6\right)^{3} \\ f^{\prime}(x)=\square \end{array}f(x)=(5x6+6)3f′(x)=□​

Problem 1510

Differentiate. y=ln⁡[(x+6)3(x+7)6(x+2)4]ddx[ln⁡[(x+6)3(x+7)6(x+2)4]]=\begin{array}{c} y=\ln \left[(x+6)^{3}(x+7)^{6}(x+2)^{4}\right] \\ \frac{d}{d x}\left[\ln \left[(x+6)^{3}(x+7)^{6}(x+2)^{4}\right]\right]= \end{array}y=ln[(x+6)3(x+7)6(x+2)4]dxd​[ln[(x+6)3(x+7)6(x+2)4]]=​

Problem 1511

Differentiate the following function. y=(ln⁡x)8+ln⁡(x8)dydx=□\begin{array}{l} y=(\ln x)^{8}+\ln \left(x^{8}\right) \\ \frac{d y}{d x}=\square \end{array}y=(lnx)8+ln(x8)dxdy​=□​ □\square□

Problem 1512

Problem 1513

t=18\mathrm{t}=18t=18 days? Answer in appropriate units.

Problem 1514

Problem 1515

Problem 1516

Problem 1517

5. [-/1 Points]DETAILS MY NOTES TANAPCALC10 6.5.0 Find the average value of the function fff over the interval [4,9][4,9][4,9]. f(x)=7−xf(x)=7-xf(x)=7−x □\square□

Problem 1518

1←1 \leftarrow \quad1← Find dydx\frac{d y}{d x}dxdy​ y=∫x1t4+5dtdydx=□\begin{array}{l} y=\int_{x}^{1} \sqrt{t^{4}+5} d t \\ \frac{d y}{d x}=\square \end{array}y=∫x1​t4+5​dtdxdy​=□​ □\square□

Problem 1519

Problem 1520

Problem 1521

Problem 1522

Calculate the left and right Riemann sums.

Problem 1523

Problem 1524

Problem 1525

(1 point)Differentiate y=1−x2sin⁡−1xy=\sqrt{1-x^{2}} \sin ^{-1} xy=1−x2​sin−1x y′=y^{\prime}=y′=

Problem 1526

Figure 1Figure 2Figure 3 (a) Which curve fits the data best? Figure 1 Figure 2 Figure 3 (b) Use the equation of the best fitting curve from part (a) to predict the speed of the object at 8 seconds. Give an exact answer, not a rounded approximation. □\square□ meters per second

Problem 1527

Find f′f^{\prime}f′, given f′(x)=1,f(x)=xsin⁡3(x2)x5+1f^{\prime}(x)=1, f(x)=\frac{x \sin ^{3}\left(x^{2}\right)}{\sqrt{x^{5}+1}}f′(x)=1,f(x)=x5+1​xsin3(x2)​

Problem 1528

Problem 1529

Problem 1530

Problem 1531

the functions f(x)=2x+3f(x)=\frac{2}{x+3}f(x)=x+32​ and g(x)=11x+2g(x)=\frac{11}{x+2}g(x)=x+211​, find the compositio tation. (f∘g)(x)=(f \circ g)(x)=(f∘g)(x)= □\square□Domain of f∘gf \circ gf∘g : □\square□

Problem 1532

Find the general antiderivative, F(x)F(x)F(x), of the function f(x)=45x9−910x10+x7f(x)=\frac{4}{5} x^{9}-\frac{9}{10} x^{10}+x^{7}f(x)=54​x9−109​x10+x7 F(x)=F(x)=F(x)=

Problem 1533

where CCC is an arbitrary constant.Find the general antiderivative, F(x)F(x)F(x), of the function f(x)=−6x724−6x107+8f(x)=-\frac{6 \sqrt[2]{x^{7}}}{4}-\frac{6 x^{10}}{7}+8f(x)=−462x7​​−76x10​+8 F(x)=F(x)=F(x)= □\square□

Problem 1534

Find the general antiderivative, F(x)F(x)F(x), of the function f(x)=2x4−6−4x5f(x)=\frac{2}{x^{4}}-6-\frac{4}{x^{5}}f(x)=x42​−6−x54​ F(x)=F(x)=F(x)=

Problem 1535

Problem 1536

f(x)={x+24<x<5x+35⩽x<6f(5)=\begin{array}{l}f(x)=\left\{\begin{array}{ll}x+2 & 4<x<5 \\ x+3 & 5 \leqslant x<6\end{array}\right. \\ f(5)=\end{array}f(x)={x+2x+3​4<x<55⩽x<6​f(5)=​

Problem 1537

3. Each side of a square is increasing at a rate of 6 cm/s6 \mathrm{~cm} / \mathrm{s}6 cm/s. At what rate is the area of the square increasing when the area of the square is 16 cm216 \mathrm{~cm}^{2}16 cm2 ?

Problem 1538

9 Mark for Review 40The function fff is defined by f(x)=x2e−x2f(x)=x^{2} e^{-x^{2}}f(x)=x2e−x2. At what values of xxx does fff have a relative maximum? (A) -2 (B) 0 (C) 1 only (D) -1 and 1

Problem 1539

Problem 1540

Sketch three different quartic functions which contain the given points: (−7,0);(−4,0);(0,5);(3,0)(-7,0) ;(-4,0) ;(0,5) ;(3,0)(−7,0);(−4,0);(0,5);(3,0)

Problem 1541

Problem 1542

Evaluate the following expression without using a calculator. log⁡6(6)\log _{6}(\sqrt{6})log6​(6​)

Problem 1543

30. For the two functions y=−2(x+5)2+qy=-2(x+5)^{2}+qy=−2(x+5)2+q and y=2(x+5)2−q,q>0y=2(x+5)^{2}-q, q>0y=2(x+5)2−q,q>0, How many times do they intersect?

Problem 1544

14. f(x)=3x3+8x2+3x−2;(x+2)f(x)=3 x^{3}+8 x^{2}+3 x-2 ;(x+2)f(x)=3x3+8x2+3x−2;(x+2)16. f(x)=8x4−24x3−x+3;(x−3)f(x)=8 x^{4}-24 x^{3}-x+3 ;(x-3)f(x)=8x4−24x3−x+3;(x−3)

Problem 1545

Question On the graph below, move the two points to graph the oblique asymptote for the function f(x)=−x2−x+1x−1f(x)=\frac{-x^{2}-x+1}{x-1}f(x)=x−1−x2−x+1​Provide your answer below: FEEDBACK MORE INSTRUCTION SUBMIT Content attribution

Problem 1546

What is the range of the sine function?The range of the sine function is □\square□ (Type your answer in interval notation.)

Problem 1547

Problem 1548

Problem 1549

Problem 1550

Problem 1551

1. Identify the parent function. Then describe the transformations that produce the graph of fff. a. f(x)=∣x+9∣f(x)=|x+9|f(x)=∣x+9∣ b. f(x)=5x3−8f(x)=5 x^{3}-8f(x)=5x3−8

The function $f(x)=9 x+7 x^{-1}$ has one local minimum and one local maximum. This function has a local maximum at $x=$ $\square$ with value $\square$ and a local minimum at $x=$ $\square$ with value $\square$

Question 7
An exponential function $f(x)=a \cdot b^{x}$ passes through the points $(0,7000)$ and $(3,56)$ . What are the values of $a$ and $b$ ? $a=$ $\square$ and $b=$ $\square$

Period: DUE: Tuesdav, 11/19/24
1. Find the volume of the solid obtained by rotating the region given about the x -axis and using the given bounds. Sketch a picture of the graph. $y=0.3 x^{3}$ , the $x-$ axis, and $x=3$

Period: DUE: Tuesdav, 11/19/24
1. Find the volume of the solid obtained by rotating the region given about the x -axis and using the given bounds. Sketch a picture of the graph. $y=0.3 x^{3}$ , the $x-$ axis, and $x=3$

Find $f^{\prime}(x)$ . $\begin{array}{l} f(x)=\left(5 x^{6}+6\right)^{3} \\ f^{\prime}(x)=\square \end{array}$

Differentiate. $\begin{array}{c} y=\ln \left[(x+6)^{3}(x+7)^{6}(x+2)^{4}\right] \\ \frac{d}{d x}\left[\ln \left[(x+6)^{3}(x+7)^{6}(x+2)^{4}\right]\right]= \end{array}$

Differentiate the following function. $\begin{array}{l} y=(\ln x)^{8}+\ln \left(x^{8}\right) \\ \frac{d y}{d x}=\square \end{array}$ $\square$

$\mathrm{t}=18$ days? Answer in appropriate units.

5. [-/1 Points]
DETAILS MY NOTES TANAPCALC10 6.5.0 Find the average value of the function $f$ over the interval $[4,9]$ . $f(x)=7-x$ $\square$

$1 \leftarrow \quad$ Find $\frac{d y}{d x}$ $\begin{array}{l} y=\int_{x}^{1} \sqrt{t^{4}+5} d t \\ \frac{d y}{d x}=\square \end{array}$ $\square$

(1 point)
Differentiate $y=\sqrt{1-x^{2}} \sin ^{-1} x$ $y^{\prime}=$

Figure 1
Figure 2
Figure 3 (a) Which curve fits the data best? Figure 1 Figure 2 Figure 3 (b) Use the equation of the best fitting curve from part (a) to predict the speed of the object at 8 seconds. Give an exact answer, not a rounded approximation. $\square$ meters per second

Find $f^{\prime}$ , given $f^{\prime}(x)=1, f(x)=\frac{x \sin ^{3}\left(x^{2}\right)}{\sqrt{x^{5}+1}}$

the functions $f(x)=\frac{2}{x+3}$ and $g(x)=\frac{11}{x+2}$ , find the compositio tation. $(f \circ g)(x)=$ $\square$
Domain of $f \circ g$ : $\square$

Find the general antiderivative, $F(x)$ , of the function $f(x)=\frac{4}{5} x^{9}-\frac{9}{10} x^{10}+x^{7}$ $F(x)=$

where $C$ is an arbitrary constant.
Find the general antiderivative, $F(x)$ , of the function $f(x)=-\frac{6 \sqrt[2]{x^{7}}}{4}-\frac{6 x^{10}}{7}+8$ $F(x)=$ $\square$

Find the general antiderivative, $F(x)$ , of the function $f(x)=\frac{2}{x^{4}}-6-\frac{4}{x^{5}}$ $F(x)=$

$\begin{array}{l}f(x)=\left\{\begin{array}{ll}x+2 & 4<x<5 \\ x+3 & 5 \leqslant x<6\end{array}\right. \\ f(5)=\end{array}$

3. Each side of a square is increasing at a rate of $6 \mathrm{~cm} / \mathrm{s}$ . At what rate is the area of the square increasing when the area of the square is $16 \mathrm{~cm}^{2}$ ?

9 Mark for Review 40
The function $f$ is defined by $f(x)=x^{2} e^{-x^{2}}$ . At what values of $x$ does $f$ have a relative maximum? (A) -2 (B) 0 (C) 1 only (D) -1 and 1

Sketch three different quartic functions which contain the given points: $(-7,0) ;(-4,0) ;(0,5) ;(3,0)$

Evaluate the following expression without using a calculator. $\log _{6}(\sqrt{6})$

30. For the two functions $y=-2(x+5)^{2}+q$ and $y=2(x+5)^{2}-q, q>0$ , How many times do they intersect?

14. $f(x)=3 x^{3}+8 x^{2}+3 x-2 ;(x+2)$
16. $f(x)=8 x^{4}-24 x^{3}-x+3 ;(x-3)$

Question On the graph below, move the two points to graph the oblique asymptote for the function $f(x)=\frac{-x^{2}-x+1}{x-1}$
Provide your answer below: FEEDBACK MORE INSTRUCTION SUBMIT Content attribution

What is the range of the sine function?
The range of the sine function is $\square$ (Type your answer in interval notation.)

1. Identify the parent function. Then describe the transformations that produce the graph of $f$ . a. $f(x)=|x+9|$ b. $f(x)=5 x^{3}-8$

10. Find $(h-g)(x)$ * 6 points $\begin{array}{l} g(x)=3 x+1 \\ h(x)=x^{3}-2 \end{array}$ $2 x^{4}-1$ $2 x^{4}+3$ Option 1 Option 2 $-x^{3}+3 x+3$ $-x^{3}+3 x-1$

8. [-/1 Points] DETAILS MẎ NOTES
Find a formula for the inverse of the given function. $\begin{array}{c} f(x)=x^{6} \\ y=\square \end{array}$ Need Help? Read It

Find the derivative of the function $f(x) = 4x e^{2x}$ , and then find the critical points of the function.

3. Using the graph of $g(x)$ shown, sketch the transformation $g(-x)+2$ on the same coordinate grid.

4. Submit answer Practice similar
Find the area bounded by the curves $y=e^{x}+1$ and $y=3 x$ over the interval $[0,1]$ . (Round your answer to two decimal places.) $\square$ Video Example: Solving A Similar Problem

2. Let $f(x)=x^{3}+5 x$ . Is $f$ even, odd, or neither? Prove your answer algebraically.

Find the derivative of the function. $\begin{array}{l} h(t)=11 \cot ^{-1}(t)+11 \cot ^{-1}\left(\frac{1}{t}\right) \\ h^{\prime}(t)=\square \end{array}$

2. Let $f(x)=\sqrt{20-x}$ and $g(x)=\sqrt{10 x-4}$ . Let $h(x)=f(x) g(x)$ . Find $h(4)$ .