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Is there a real function that is differentiable at any point but nowhere monotone?

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    the constant function works, but I assume that example should be disallowed.2011-01-11
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    Doesn't "monotone" by default mean weakly, not strictly, monotone? (i.e. monotone increasing means for all $x$, $y$, $x \le y \Rightarrow f(x) \le f(y)$). So constant functions are everywhere monotone.2011-01-11
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    See also the [MO version](http://mathoverflow.net/q/167323/6085) of this question for additional details and references.2014-05-16
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    And see [here](http://math.stackexchange.com/a/802647/462) for details of the Katznelson-Stromberg construction.2014-05-21

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Yes. See for example "Everywhere Differentiable, Nowhere Monotone, Functions" by Y. Katznelson and Karl Stromberg.

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    The link doesn't work; is it just me?2011-11-20
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    @Jonas: Google katznelson-stromberg.pdf and then click on "Quick view" on the first result.2011-11-20
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    The link above seems broken as well. Anyway, details have been posted [here](http://math.stackexchange.com/a/802647/462).2014-05-21