analysis question

. , Suppose that f is analytic on and inside |z| S 2. Suppose also that that f(0) : 0, f'(0) = 0, and that |f(z)| S 4 for all |z| S 2. \":0 if 2: 7E 0 and Show that F(z) : Z is analytic on and inside |z| S 2. f\"(0) .f 0 1 2: : 2