General theorem about all inflection points Let $f$ be a function. I know that, if $c\in dom(f)$ and either $f''(c)=0$ or $f''(c)$ is undefined, then $c$ may be an inflection point. Can there be inflection points such that $c\in dom(f)$ and $f''(c)\not=0$ and $f''(c)$ is defined?

No, the vanishing of the second derivative is a necessary condition for $c$ to be an inflection point (provided we are assuming $f''(c)$ is defined.) 
This condition is not sufficient, as can be seen with $c=0$ and $f(x) = x^4$. 
