Question

What is the instantaneous rate of change of `f(x)=(x-2)^3` at `x=3`?

Answer 1

I found: `3`

Explanation:

The instantaneous rate of change will be the derivative evaluated at that point:

`f'(x)=3(x-2)^2` Using the Chain Rule:

and at `x=3`:

`f'(3)=3(3-2)^2=3`