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Need a little help in the following:

Let $f(z)$ analytic function on $D = \{z\in\mathbb C: |z| < 1\}$. Define $\displaystyle d = \sup_{z,w \in D} |f(z) - f(w)|$.

Prove that $|f'(0)| \leq \frac{d}{2}$.

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