The following is a multiple choice question in which more than one option may be right.

Let D={z belongs to C: |z| <1} which of the following is true?

a) There exists a holomorphic function f from D->D with f(0)= 0, f'(0)=2

b) There exists a holomorphic function f from D->D with f(3/4)= 3/4, f'(2/3)=3/4

c) There exists a holomorphic function f from D->D with f(3/4)= 3/4, f ' (3/4)= -3/4

d) There exists a holomorphic function f from D->D with f(1/2)= -1/2, f ' (1/4)= 1

I've used Schwarz-Pick Theorem and Schwarz lemma to confirm that the first(a) and the third(c) options are right. But I'm not able to ascertain whether options b and d are right or not.

Can some one throw some light on that?

Thanks