Give an example of a function f(x)

Question

For which f '(0) exists, but f ''(0) does not exist, and explain why:

Trick question that I cant seem to solve.

This is a duplicate, but I haven't the time to look for it now. — Cameron Buie, Oct 30 '15 at 02:33
https://math.stackexchange.com/questions/78825/example-of-a-function-that-is-not-twice-differentiable?rq=1 — zahbaz, Oct 30 '15 at 02:46

score 0 · Answer 1 · answered Oct 30 '15 at 02:39

0

Which function you know is continuous but not differentiable at 0? It's anti-derivative will be differentiable once but not twice at 0.

answered Oct 30 '15 at 02:39

Amey Deshpande

score 0 · Answer 2 · answered Oct 30 '15 at 02:43

You know that $f(x)=|x|$ is not differentiable at 0. Integrate it, $F(x)=-\frac{x^2}{2}$ if $x<0$ and $F(x)=\frac{x^2}{2}$ if $x >= 0$.

It is an example, there are a lot of other example, some more interessting i suppose, maybe with sinus and a fraction.

2 Answers2