TITLE: Function example? Continuous everywhere, differentiable nowhere
QUESTION [5 upvotes]: Possible Duplicate:
Are Continuous Functions Always Differentiable? 

If such a function exists, can anyone give an example of a function $f(x) : \mathbb{R} \longrightarrow \mathbb{R}$  that is continuous for all $x \in \mathbb{R}$ but differentiable nowhere?

REPLY [7 votes]: Another popular example is what I know as Takagi's Function.
It is somehow different from the Weierstrass Function in that it is not constructed as a uniform limit of differentiable functions. However, it is a uniform limit of continuous functions in a way that the points of non-differentiability populate the "whole interval" (if that point of view makes any sense...).

REPLY [6 votes]: A very famous example - and by far the most important when it comes to practical applications (finance: option pricing!) - is the Wiener process.