Question: 2. (6 points) Three facts about Lipschitz functions: (a) Show that if f : R - R is Lipschitz, then it is uniformly continuous. (b)

2. (6 points) Three facts about Lipschitz functions: (a) Show that if f : R - R is Lipschitz, then it is uniformly continuous. (b) True or false - if f : R - R is continuous, bounded, and differentiable, then it is Lipschitz. (c) Let I = [a, b] be a closed bounded interval. Consider f E C'(I). Show that the Lipschitz constant of f on I is exactly M = maxxer If'(x) |. By Lipschitz constant we meed the minimal constant L > 0 for which the Lipschitz continuity inequality holds for all x, y E

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