Let $$f: [2, 4] \to \mathbb{R}$$ be a differentiable function such that $$x\log_e xf'(x) + \log_e xf(x) + f(x) \geq 1$$, $$x \in [2, 4]$$ with $$f(2) = \frac{1}{2}$$ and $$f(4) = \frac{1}{2}$$.
Consider the following two statements:
(A) $$f(x) \leq 1$$, for all $$x \in [2, 4]$$
(B) $$f(x) \geq 1/8$$, for all $$x \in [2, 4]$$
Then,

A

Neither statement (A) nor statement (B) is true

B

Only statement (B) is true

C

Both the statements (A) and (B) are true

D

Only statement (A) is true