Math Help - Complex Analysis -analytic function

1. Complex Analysis -analytic function

Hello!
Help me with this problem please.

Thanks!

Let $f(z)$ be an analytic function in $D=\left \{ z:\left | z \right | <1\right \}$.
Assume that $d=\underset{z,w\in D}{sup} \left | f(z)-f(w) \right |$.

Prove that: $\left | f'(0) \right |\leqslant d/2$

2. Re: Complex Analysis -analytic function

Hint Use the Cauchy inequalities to $g(z)=f(z)-f(0)$ for $n=1$.