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

Jun 1, 2018

$x \approx 0.2397184192$

#### Explanation:

Writing $f \left(x\right)$ in the following form
$f \left(x\right) = x \cdot {e}^{- x - {x}^{2}} - {x}^{2}$
so
$f ' \left(x\right) = {e}^{- x - {x}^{2}} + x \cdot {e}^{- x - {x}^{2}} \left(- 2 x - 1\right) - 2 x$
this equation can only be solved by a numerical method:
$x \approx 0.2397184192$