Question

What is the average or mean slope of the function `2x^3 - 6x^2 - 48x + 4` on the interval [-4,9]?

Answer 1

The mean slope (aka the average rate of change) of `f` on `[-4,9]` is `(f(9)-f(4))/(9-(-4))`

Explanation:

For `f(x) = 2x^3 - 6x^2 - 48x + 4`, we have
`f(-4) = -28` `" "` and `" "` `f(9)=544`

So the mean slope is

`(f(9)-f(4))/(9-(-4)) = (544-(-28))/(9-(-4))`

`= 572/13 = 44`