# A continuous, monotone nowhere function [closed]

Please give an example of a continuous function f:[a,b]->R (a,b are real nos.), such that there is no open subinterval of [a,b],where f is monotone. Here, the constant function is considered monotone.

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–  Michael Greinecker Dec 18 '11 at 16:01
To be clear, every function monotone on an open interval is differentiable almost everywhere there. So any example of a continuous, nowhere-differentiable function will do. –  Michael Greinecker Dec 18 '11 at 16:10
If you want an everywhere differentiable function, see artofproblemsolving.com/Forum/viewtopic.php?f=70&t=2822 In any case, this is neither a research level question, nor something amusing enough to make one tempted to ignore the proclaimed MO rules. So, I'm voting to close. –  fedja Dec 18 '11 at 16:27