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

1. Jul 14, 2008

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

2. Jul 14, 2008

### Gear300

Re: function

The slope erratically changes.

3. Jul 14, 2008

### uman

4. Jul 15, 2008

### roam

Re: function

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

5. Jul 15, 2008

### matticus

Re: function

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

6. Jul 16, 2008

### fedaykin

Re: function

$$f(x)= sin (\fraction\pi/x)$$
$$f(x) = |x|$$
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.

Last edited: Jul 16, 2008