### Solve the problems using differentiability of real analysis.

These problems are real analysis related problems. One of these is Liptuaz continuity/holder condition. It would be nice if you use mean value theorem for solving that problem. 1. Let f : [0, 2] ? R be continuous, assume that f is twice differentiable at all points of (a, b), and assume that f(0) = 0, f(1) = 1 and f(2) = 2. P