Question

How do you find the average rate of change of `f(x)=2x^2+2` from -3 to 0?

Answer 1

`-6`

Explanation:

Average rate of change is given by the formula:
`(f(b)-f(a))/(b-a)`

In our case, `b=-3` and `a=0`. First, we find `f(b)` and `f(a)`:
`f(b)=f(-3)=2(-3)^2+2=20`
`f(a)=f(0)=2(0)^2+2=2`

Plugging all the info into the formula:
`(20-2)/(-3-0)=18/-3=-6`.
The negative sign means the function is decreasing over the interval.