Let $ f : D \rightarrow D $ be holomorphic with $ f(0) = \frac{1}{2}$ and $ f(\frac{1}{2}) = 0 $, where $ D = \{ z : |z|\leq 1 \} $. Please suggest which of the following can be correct ..
$ |f'(0)|\leq \frac{3}{4}$.
$ |f'(1/2) |\leq \frac{4}{3}$.
$ |f'(0)|\leq \frac{3}{4}$ and $ |f'(1/2)|\leq \frac{4}{3}$.
$ f(z)=z$, $ z\in D$
Please help.