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edited Jul 5, 2022 at 21:21

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Let $$f_\pm(x):=e^x(1\pm c\sin x)$$ for some $c\in(0,1/2]$ and all real $x$.

Then $f_+$ and $f_-$ are increasing differentiable convex functions that agree exactly on the countable set $\pi\mathbb Z$.

answered Jul 5, 2022 at 21:15

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