31.6 An older proof of Theorem 31.3 goes as follows, which we outline for c = 0. Assume x > 0, let M be as in the proof of Theorem 31.3, and let F(t) = f(t) + n −1 k=1 (x − t)k k! f(k) (t) + M · (x − t)n n! for t in [0, x]. Show F is differentiable on [0, x] and F (t) = (x − t)n−1 (n − 1)! [f(n) (t) − M].