Consider a homeomorphism of the real line $F : \mathbb{R} \to \mathbb{R}$ such that it is differentiable everywhere and the derivative is bounded. Does it follow that the derivative is continuous, even at a single point?
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4$\begingroup$ Yes, see here math.stackexchange.com/questions/1444138/… and second answer in math.stackexchange.com/questions/292275/… $\endgroup$– Thomas KojarCommented Mar 13, 2023 at 23:32
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$\begingroup$ Thanks, and sorry for asking a duplicate question. $\endgroup$– Andy HammerlindlCommented Mar 14, 2023 at 1:28
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