Let $f:(0, \infty) \rightarrow \mathbb{R}$ be a function defined as $f(x)=\frac{x e^{-x}}{1+x}$. Then

• A

  $f$ is a strictly decreasing function on $(0, \infty)$
• B

  $f$ is a surjective function
• C

  $f$ is a strictly increasing function on $(0, \infty)$
• Correct answer
  D

  there exists a unique $x_0 \in(0, \infty)$ such that $f\left(x_0\right) f^{\prime \prime}\left(x_0\right) \lt 0$

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