Let $f(x)=|x|x$ then $f''(0)$ does not exist.
Why?
If $x>0$, $f'(x)=2x$ and if $x<0$, $f'(x)=-2x$.
Then when $x=0$, does $f'(x)$ also not exist?
Let $f(x)=|x|x$ then $f''(0)$ does not exist.
Why?
If $x>0$, $f'(x)=2x$ and if $x<0$, $f'(x)=-2x$.
Then when $x=0$, does $f'(x)$ also not exist?