Non-differentiable function

1. Sep 18, 2012

damabo

I know that $e^{rx}$ is an infinitely differentiable function.
However, say you have f= x. this is clearly one time differentiable, giving 1. a second time it can be derived as well, giving 0. is 0 differentiable, indeed differentiation gives zero.
So when is a function non-differentiable. i'm thinking of cusps, such as on x=0 with the function f=|x|, or other functions where the derivative is undefined. correct? are there other cases? it would also be interesting to see a function that is only finitely differentiable.

Last edited: Sep 18, 2012
2. Sep 18, 2012

pwsnafu

3. Sep 18, 2012

damabo

that's a nice one!

4. Sep 18, 2012

chiro

5. Sep 18, 2012

damabo

thanks, will apply that formula.