Question

Is `f(x)=xe^(x^3-x)-x^3` increasing or decreasing at `x=4`?

Answer 1

It is increasing.

Explanation:

In order to find out, you need the derivative of f.

`f'(x) = e^(x^3 - x) + x(3x^2 - 1)e^(x^3 - x) -3x^2` by the product and sum rules.

You know calculate`f'(4)`, which here equals to `e^(60) + 188e^(60) -48` which is obviously positive.