Question

How do you find the average rate of change of `f(x) = 4x^3 - 8x^2 - 3` from -5 to 2?

Answer 1

`100`

Explanation:

The average rate of change of a function on the interval `a` to `b` is

`"average rate of change"=(f(a)-f(b))/(a-b)`

Here, this gives us

`"average rate of change"=(f(-5)-f(2))/(-5-2)`

We can find the function values individually:

`f(-5)=4(-5)^3-8(-5)^2-3=-703`

`f(2)=4(2)^3-8(2)^2-3=-3`

Thus,

`"average rate of change"=(-703-(-3))/(-7)=(-700)/(-7)=100`