Question for finding bound for $f'(z)$[CSIR-December 2011]

Take $f(z)=z^2$ for which $|f'(3/4)|=3/2\ge 1$. So (c) is false.

Option (d) is true by using Schwarz Pick theorem,

$|f'(0)|\leq \frac{1-|f(0)|^2}{1-|0|^2}=1-|f(0)|^2\leq 1$

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Complex Analysis

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