Question

Is `f(x)=4xe^x` increasing or decreasing at `x=-2`?

Answer 1

It's decreasing.

Explanation:

In order to know, you calculate the derivative of `f` and you evaluate it at `-2`.

By the product rule, `f'(x) = 4e^x + 4xe^x`.

We now evaluate `f'(2) = 4e^(-2) -8e^(-2) = 4/e^2 - 8/e^2 = -4/e^2 < 0` becase `e^2 > 0`. So `f` is decreasing at `x = -2`.