a) False. At $+\infty$, the function is open, hence, it can not be bounded.
b) False. Only if $f'(x) > 0$ for all $x$ can we say that $f$ is increasing. This is not mentioned. What we know is that $f'(x)$ is positive near $+\infty$. So it could be the case that $f$ is decreasing near some value of $x$.
d) False. The function $f$ can have infinite slope for some $x$.
Ans- C