Let $$f(x) = 2x + \tan^{-1}(x)$$ and $$g(x) = \log_e(\sqrt{1+x^2} + x), \quad x \in [0, 3]$$. Then

A

There exists $$x \in [0, 3]$$ such that $$f'(x) < g'(x)$$

B

$$\max f(x) > \max g(x)$$

C

There exist $$0 < x_1 < x_2 < 3$$ such that $$f(x) < g(x), \forall x \in (x_1, x_2)$$

D

$$\min f'(x) = 1 + \max g'(x)$$