The function $f(x)=x e^{-x} \forall x \in \mathbb{R}$ attains a maximum value at $x=k$, then $k=$

• Correct answer
  A

  $1$
• B

  $2$
• C

  $\frac{1}{\mathrm{e}}$
• D

  $3$

Hence, the correct answer is option: 'A'.