Studdy AI Logo
Math

QuestionCalculate the average rate of change of f(x)=−2x+17f(x) = -2x + 17 from x1=0x_1 = 0 to x2=3x_2 = 3.

Studdy Solution

STEP 1

Assumptions1. The function is f(x)=−x+17f(x) = -x +17 . The initial x-value is x1=0x_{1} =0
3. The final x-value is x=3x_{} =3
4. The average rate of change of a function from x1x_{1} to xx_{} is given by the formulaAverage rate of change=f(x)−f(x1)x−x1Average\, rate\, of\, change = \frac{f(x_{}) - f(x_{1})}{x_{} - x_{1}}

STEP 2

First, we need to find the value of the function at x1x_{1} and x2x_{2}. Let's start with x1x_{1}.
f(x1)=f(0)=−2(0)+17f(x_{1}) = f(0) = -2(0) +17

STEP 3

Calculate the value of the function at x1x_{1}.
f(x1)=−2(0)+17=17f(x_{1}) = -2(0) +17 =17

STEP 4

Now, find the value of the function at x2x_{2}.
f(x2)=f(3)=−2(3)+17f(x_{2}) = f(3) = -2(3) +17

STEP 5

Calculate the value of the function at x2x_{2}.
f(x2)=−2(3)+17=11f(x_{2}) = -2(3) +17 =11

STEP 6

Now that we have the values of the function at x1x_{1} and x2x_{2}, we can find the average rate of change of the function from x1x_{1} to x2x_{2} using the formulaAverage rate of change=f(x2)−f(x1)x2−x1Average\, rate\, of\, change = \frac{f(x_{2}) - f(x_{1})}{x_{2} - x_{1}}

STEP 7

Plug in the values for f(x2)f(x_{2}), f(x1)f(x_{1}), x2x_{2}, and x1x_{1} to calculate the average rate of change.
Average rate of change=11−173−0Average\, rate\, of\, change = \frac{11 -17}{3 -0}

STEP 8

Calculate the average rate of change of the function.
Average rate of change=11−173−0=−2Average\, rate\, of\, change = \frac{11 -17}{3 -0} = -2The average rate of change of the function from x1x_{1} to x2x_{2} is -2.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord