Question

What is the instantaneous rate of change of `f(x)=(x^2-2)e^(x+2 )` at `x=1`?

Answer 1

`f'(1)=e^3`

Explanation:

The instantaneous rate of change is the same as the derivative of the function.

We need the product rule to differentiate this function and using it gives

`f'(x)=(x^2-2)e^(x+2)+2xe^(x+2)`

`therefore f'(1)=(1-2)e^3+2e^3`

`=e^3`