Problem

Part I Multiple Choice

1. Let $f$ be a smooth function on $\mathbb{R}$.

(a) If $f''>0$ on $\mathbb{R}$, then $f'$ must be increasing on $\mathbb{R}$.

(b) If $f''>0$ on $\mathbb{R}$, then $f$ must be concave upward on $\mathbb{R}$.

(c) If $f''(a)=0$, then the point $(a,f(a))$ must be an inflection point.

Among the above three statements, how many of them are true?

A) Only one.

B) Only two.

C) All of them.

D) None of them.