Suppose $f$ is a function which has a sharp point at $c$ and hence not differentiable at $c$.Can there be found such $f$ which satisfies the above property but is invertible and its inverse is differentiable on its domain? A related question also occurs in my mind that can I construct a strictly monotone function on $\mathbb R$ differentiable at only one point?
2026-03-26 17:44:40.1774547080
Can I get a function having a sharp point but its inverse differentiable on its domain.
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On the last question: No, a monotone function is differentiable almost everywhere.