# continuous function and not differentiable [duplicate]

Possible Duplicate:
Function example? Continuous everywhere, differentiable nowhere

Is there any function that continuous in all places and not differentiable in all places?

 I added the reference-request tag as you ask for a book. – Hagen von Eitzen Dec 1 '12 at 17:59 Nice additional information: A randomly chosen continuous function is nearly "always" not differentiable in all places. For example the continous functions on $\left[0,1\right]$ that are not differentiable in all places are dense in all continous function on $\left[0,1\right]$ – Fant Dec 1 '12 at 18:15