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> (Tao Volume 2, P.152, Exercise 6.6.3) Give an example of a function $f: [a,b] \to \mathbb{R}$ which is continuously differentiable and such that $|f(x) - f(y)| < |x-y|$ for all $x,y \in [a,b]$, but such that $|f'(x)| = 1$ for at least one value of $x \in [a,b]$.
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I am struggling to coming up with an example. Could you give me one?