Let $$f : R \rightarrow (0, \infty)$$ and $$g : R \rightarrow R$$ be be twice differentiable functions such that $$f''$$ and $$g''$$ are continuous functions on R. Suppose $$f'(2) = g(2) = 0, f''(2) \neq 0$$ and $$g'(2) \neq 0$$. If $$\lim_{x \rightarrow 2}\frac{f(x)g(x)}{f'(x)g'(x)} = 1$$, then

A

f has a local minimum at x = 2

B

f has a local maximum at x = 2

C

$$f''(2) > f(2)$$

D

$$f(x) - f''(x) = 0$$ for at least one $$x \epsilon R$$.