Question

How to find instantaneous rate of change for `f(x)=x^3+x^2` at (2, 12)?

Answer 1

The instantaneous rate of change is given by the derivative.

Explanation:

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

At `x=2`, the instantaneous rate of change is

`f'(2) = 3(2)^2+2(2) = 16`

Units are `"units of " f`/`"units of "x`