# What are the critical points of f(x) =1/(xe^x)-e^(2x)/x?

##### 1 Answer
Jun 4, 2017

$\text{f} \left(x\right) = \frac{1 - {e}^{3 x}}{x {e}^{x}}$

By using the series for the exponential function,

"f"(x)=(1-(1+3x+(3x)^2/2!+...))/(x+x^2+x^3/2!+...)

"f"(x)=(3x+(3x^2)/2!+...))/(x+x^2+x^3/2!+...)

"f"(x)=(3+9x/2!+...)/(1+x+...)

Then as $x \setminus \to 0$, $\text{f} \left(x\right) \setminus \to 3$.