Question

What are the critical values of `f(x)=x/e^(x+x^2)-x^2`?

Answer 1

`xapprox 0.2397184192`

Explanation:

Writing `f(x)` in the following form
`f(x)=x*e^(-x-x^2)-x^2`
so
`f'(x)=e^(-x-x^2)+x*e^(-x-x^2)(-2x-1)-2x`
this equation can only be solved by a numerical method:
`xapprox 0.2397184192`