Question

How do you find the average rate of change of `y=x^2+2` over [-2,-3/2]?

Answer 1

`-7/2`

Explanation:

The average rate of change of a function `y` over the interval `[a,b]` is given by the slope of the secant line connecting these two points on the graph of `y`, or:

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

Here, on the interval `x in[-2,-3/2]`, we see that the average rate of change will be given by:

`(y(-3/2)-y(-2))/(-3/2-(-2))`

First we can find the value of the function at these points:

`y(-3/2)=(-3/2)^2+2=9/4+2=17/4`

`y(-2)=(-2)^2+2=4+2=6`

Then the average rate of change equals:

`(17/4-6)/(-3/2-(-2))=(-7/4)/(1/2)=-7/2`