Question

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

Answer 1

I found `44.334`

Explanation:

The instantaneous rate of change is the derivative of our function (which is the rate of change) evaluated at the specific point (at `x=2`).

So we get:

`f'(x)=(2x)e^x+(x^2-2)e^x` using the Product Rule.

Evaluate it at `x=2` to get:

`f'(2)=4e^2+2e^2=6e^2=44.334`