Discussion Forum



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 B

Explanation:

f'(x)  is increasing

 For some x in ($\frac{1}{2},1$)

f'(x)=1

f'(1)>1