#### glittergal96

##### Active Member

- Joined
- Jul 25, 2014

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- HSC
- 2014

Being differentiable is also a "niceness" property at a point. In fact it is a much stronger property, in the sense that differentiability at a point implies continuity at a point.

It is clearly possible to find functions that are continuous but not everywhere differentiable (absolute value function fails to be differentiable at 0).

What is surprising (well, I find it surprising, and the discovery went against the beliefs at the time) is that there exist a function that is continuous everywhere and differentiable

*nowhere*! : https://en.wikipedia.org/wiki/Weierstrass_function

In fact, in a certain sense, MOST continuous functions are differentiable nowhere!