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Suppose $f:D(0,1) \longrightarrow \mathbb{C}$ is holomorphic, where $$D(0,1) = \{z \in \mathbb{C} \mid |z|<1\},$$ and assume the maximum $|f(z)| \le 2$.

Estimate: $|f^{(3)}(i/3)|$.

I have the solution to this problem which used $R=2/3$.

I am not sure how to find this $R$ because I don't understand the Cauchy Estimate that well. Any help to understand this problem will be real helpful thank you.

2 Answers 2