Question: Suppose that f' is integrable and |f'(x)| M for all x. Prove that |f(x)| |f(a)| +M|x -a| for every a.

Suppose that f' is integrable and |f'(x)| ≤ M for all x. Prove that |f(x)| ≤ |f(a)| +M|x -a| for every a.

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