Question: A function f is convex on [a, b] if f(tx + (1-t)y) 0, prove that f is convex in an interval about xo. (c) If

A function f is convex on [a, b] if f(tx + (1-t)y) 0, prove that f is convex in an interval about xo. (c) If f E C2 [a, b] and f" (x) 2 0 for all x E (a, b), show that f is convex on [a, b]

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