Observe the statements given below :
Assertion $(A)$ : $f(x)=x e^{-x}$ has the maximum at $x=1$
Reason $(R)$ : $f^{\prime}(1)=0$ and $f^{\prime \prime}(1) < 0$
Which of the following is correct?

• A
  Both $(A)$ and $(R)$ are true and $(R)$ is the correct reason for $(A)$
• B
  Both $(A)$ and $(R)$ are true, but $(R)$ is not the correct reason for $(A)$
• C
  $(A)$ is true, $(R)$ is false
• D
  $(A)$ is false, $(R)$ is true