Observe the statement given below: Assertion (A): $f(x)=x e^{-x}$ has the maximum at $x=1$ Reason (R): $f(1)=0$ and $f(1) <0$ which of 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

(a) Both (A) and (R) are true and (R) is the correct reason for (A)