Question

Find the average rate of change of the function

Answer 1

Average rate of change=change in f(x)/ change in x=(f(x₂)-f(x₁)) / (x₂-x₁)
Data:
f(x)=x²+3x
x₁=4
x₂=9

Average rate of change=((9²+3*9) - (4²+3*4)) / (9-4)=
=((81+27)-(16+12)) / (9-4)=
=(108-28)/5=80/5=16.

Answer: The average rate of change is 16.

Answer 2

The average rate of change from an interval from
`x_1` to
`x_2` is the change in the value of the function divided by the change in x.


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

Let's find the values of
`f(x_1)` and
`f(x_2)`


`f(x_1)=4^2+3(4)=28`

`f(x_2)=9^2+3(9)=108`


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


`=(108-28)/(9-4)=\boxed{16}`

Your answer is 16. I hope this helps and have an awesome day! :)