If $$f:R\rightarrow R$$is a twice differentiable function such that $$f''(x)>0$$ for all $$x\epsilon R$$, and $$f(\frac{1}{2})=\frac{1}{2},f(1)=1$$, then

A

$$f'(1)\leq0$$

B

$$0<f'(1)\leq\frac{1}{2}$$

C

$$\frac{1}{2}<f'(1)\leq\ 1$$

D

$$f'(1)>1$$