Question

How do you find the average rate of change of `y=-x^2+4` over [1,5]?

Answer 1

`(y(5)-y(1))/(5-1)=(-21-3)/4=-6`

Explanation:

The average change of `y` over the interval `[a,b]` is given by:

`(y(b)-y(a))/(b-a)`

Here, we see that:

`y(5)=-5^2+4=-21`

`y(1)=-1^2+4=3`

So the average rate of change is:

`(y(5)-y(1))/(5-1)=(-21-3)/4=-6`