Example a function that is continuous at every point but not derivable

[hadi amiri 4]

can you example a function that is continuous at every point but not derivable

 

[Gear300]

The slope erratically changes.

 

[uman]

http://en.wikipedia.org/wiki/Weierstrass_function

 

[roam]

Yes, I also think of the weierstrass function is a perfect example of that.

 

[matticus]

I was thinking the dirichlet function, but that's the one that's discontinuous everywhere.

 

[fedaykin]

$$f(x)= sin (\fraction\pi/x)$$
$$f(x) = |x|$$
The problem's ambiguity at x=0.

Any interval on a curve where the derivative would divide by zero. $$f(x) = \sqrt[3]{x}$$ would do this at x=0.

Edit* I'm sorry if you were looking for functions that are not differentiable on any interval but are continuous.