Let $$f(x) = \lim_{n \rightarrow \infty}\left(\frac{n^n(x + n)\left(x + \frac{n}{2}\right).........\left(x + \frac{n}{n}\right)}{n!(x^2 + n^2)\left(x^2 + \frac{n^2}{4}\right).........\left(x^2 + \frac{n^2}{n^2}\right)}\right)^{\frac{x}{n}}$$, for all x > 0. Then

A

$$f\left(\frac{1}{2}\right) \geq f(1)$$

B

$$f\left(\frac{1}{3}\right) \leq f\left(\frac{2}{3}\right)$$

C

$$f'(2) \leq 0$$

D

$$\frac{f'(3)}{f(3)} \geq \frac{f'(2)}{f(2)}$$