Is it true that $ \lim_{x\to0}\frac{f'\left(x\right)-\frac{f\left(x\right)-f\left(0\right)}{x}}{x}=\frac{f''\left(0\right)}{2} $
Let f be a function twice differentiable and with derivatives continuous on an interval $[a,b]$ containing $0$. Prove the following statement: