Complex Analysis Problem regarding holomorphic funtions

Question

let $f$ be a holomorphic function on a domain containing the closer of the unit disk, such that $|f(z)|\leq 5$ on $|z|=1$ then if $f(0)=3+4i$ find $f'(0)$

Hint, please. can I determine the exact form of the function? By using Rouche's theorem I can only say that $f$ a zero inside the unit circle.

Answer 1

Hint: Maximum modulus principle.