Question

How do you find the average rate of change for the function `f (z) = 5 - 8z^2` on the indicated intervals [-8,3]?

Answer 1

40

Explanation:

The `color(blue)"average rate of change"` of f(z)over an interval between 2 points (a ,f(a) and (b ,f(b) is the slope of the `color(blue)"secant line"` connecting the 2 points.

To calculate the average rate of change between the 2 points.

`color(red)(|bar(ul(color(white)(a/a)color(black)((f(b)-f(a))/(b-a))color(white)(a/a)|)))`

here a = - 8 and b = 3

`rArrf(-8)=5-8(-8)^2=-507`

and `f(3)=5-8(3)^2=-67`

The average rate of change between (-8 ,-507) and (3 ,-67) is

`(-67-(-507))/(3-(-8))=(440)/(11)=40`

This means that the average of all the slopes of lines tangent to the graph of f(z) between (-8 ,-507) and (3 ,-67) is 40.