1) If $f:R\rightarrow R$ is twice differentablr function such that f''(x)>0, for all xε R, and $f(\frac{1}{2})=\frac{1}{2}$ , f(1)=1, then A) $f''(1)\leq0$ B) $f'(1)>1$ C) $0\lt f'(1) \le \frac{1}{2}$ D) $\frac{1}{2}\lt f'(1) \le 1$ Answer: Option BExplanation:f'(x) is increasing For some x in ($\frac{1}{2},1$) f'(x)=1 f'(1)>1
