Let $f : [0,2] \rightarrow \mathbb{R}$ be a continuous function such that
$$\frac{1}{2}\int_0^2 f(x)\,dx < f(2)$$
Then which of the following statements must be true?\\
(A) $f$ must be strictly increasing.\\
(B) $f$ must attain a maximum value at $x = 2$.\\
(C) $f$ cannot have a minimum at $x = 2$.\\
(D) None of the above.