QuestionFind the average rate of change of $f(x)=6x+9$ from $x_1=3.5$ to $x_2=9$ , rounded to the nearest whole number.

Studdy Solution

STEP 1

Assumptions1. The function is $f(x)=6x+9$ . We are looking for the average rate of change from $x_{1}=3.5$ to $x_{}=9$

STEP 2

The average rate of change of a function $f(x)$ from $x_{1}$ to $x_{2}$ is given by the formula $Average\, rate\, of\, change = \frac{f(x_{2}) - f(x_{1})}{x_{2} - x_{1}}$

STEP 3

First, we need to find the values of $f(x_{1})$ and $f(x_{2})$ . We can do this by substituting $x_{1}$ and $x_{2}$ into the function $f(x)$ .
$f(x_{1}) =6x_{1} +9$ $f(x_{2}) =6x_{2} +9$

STEP 4

Substitute the given values for $x_{1}$ and $x_{2}$ into the equations to find the values of $f(x_{1})$ and $f(x_{2})$ .
$f(x_{1}) =6(3.) +9$ $f(x_{2}) =6(9) +9$

STEP 5

Calculate the values of $f(x_{1})$ and $f(x_{2})$ .
$f(x_{1}) =(3.5) +9 =30$ $f(x_{2}) =(9) +9 =63$

STEP 6

Now that we have the values of $f(x_{1})$ and $f(x_{2})$ , we can substitute these into the formula for the average rate of change.
$Average\, rate\, of\, change = \frac{f(x_{2}) - f(x_{1})}{x_{2} - x_{1}}$ $Average\, rate\, of\, change = \frac{63 -30}{9 -3.5}$

STEP 7

Calculate the average rate of change.
$Average\, rate\, of\, change = \frac{33}{5.5} =6$ The average rate of change of $f(x)$ from $x_{1}=3.5$ to $x_{2}=9$ is6.

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

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

Parents Influencer program Contact Policy Terms