Question

What are the values and types of the critical points, if any, of `f(x)=e^(-2x^2)-xe^x`?

Answer 1

`P_max(-0.182115825969939296277,1.087614208523047937841)`

Explanation:

We get
`f'(x)=-e^(-2x^2)(e^(x+2x^2)+4x+e^(x+2x^2)x)`
By a numerical method we get
`x_1approx -0.182115825969939296277`
and
`f''(x)=-e^(-2x^2)(4+2e^(x+2x^2)+e^(x+2x^2)x-16x^2)`
and

`f''(x_1)<0`
so we get a maximum.