Question

How do you find the average rate of change of `f(x)=x^2+2` over [-2,1]?

Answer 1

`-2/3`

Explanation:

This is equivalent to asking for the average slope of the function between the 2 endpoints.

So we can find the function values at the 2 endpoints and then join the 2 and find the gradient of the straight line joining them.

`f(-2)=(-2)^2+2=6`
`f(1)=1^2+2=3`

Thus gradient `m=(Deltay)/(Deltax)=(3-6)/(1-(-2))=-2/3`