Question

Find the average rate of change for f(x) = x2 + 9x + 18 from x = 10 to x = 20.

Answer 1

First, plug x=10 and x=20 into the formula:
10^2+90+18
190+18
208

20^2+180+18
400+198
598

598-208=390

390/10 = 39

The average rate of change is 39

Answer 2

The average rate of change for f(x) from x = 10 to x = 20 is 39.

Explanation:

The given function is

`f(x)=x^2+9x+18`

`f(10)=(10)^2+9(10)+18=208`

`f(20)=(20)^2+9(20)+18=598`

The formula for average rate of change for a function is

`m=(f(x_2)-f(x_1))/(x_2-x_1)`

We have to find the average rate of change for f(x) from x = 10 to x = 20.

`m=(f(20)-f(10))/(20-10)`

`m=(598-208)/(10)`

`m=(390)/(10)`

`m=39`

Therefore the average rate of change for f(x) from x = 10 to x = 20 is 39.