let $f:\mathbb{R} \rightarrow \mathbb{R}$ be a strictly increasing function. Then which one of the following is always true?
A) The limits $\lim_{x\rightarrow a+} f(X)$ and $\lim_{x\rightarrow a-} f(X)$ exist for all real number a
B) if $f$ is differentiable at a then $f'(a)>0$
C) There cannot not be a real number $B$ such that $f(x) < B$ for all real $x$
D) There cannot not be a real number $L$ such that $f(x) > L$ for all real $x$