Let [tex]\displaystyle f(x)= \lim_{n\to \infty}\left( \dfrac{n^n (x+n)\left(x+\dfrac{n}{2}\right) \dots \left(x+\dfrac{n}{n}\right)}{n! (x^2+n^2)\left(x^2+\dfrac{n^2}{4}\right)\dots \left( x^2+\dfrac{n^2}{n^2}\right)}\right)^{\dfrac{x}{n}}[/tex] for all x > 0 , then;

[tex] A ) \ f\bigg(\dfrac{1}{2}\bigg) \leq f(1) \\\\ B)\ f\bigg(\dfrac{1}{3}\bigg) \geq f\bigg(\dfrac{2}{3}\bigg) \\\\ C) \ f'(2)\geq 0 \\\\ D) \ \dfrac{f'3(3)}{f(3)}\leq \dfrac{f'(2)}{f(2)} [/tex]​