[10] Suppose f is differentiable on [0,1] and that f (:5) 6 [0,1] for each :1; E [0,1]. Show there exists a point c with at) = c. If further, f'($) 76 1 for any :1: 6 [0,1] show that there is exactly one such number a. Show that (am/2 + sinx 2 1 for all x Z 0