General theorem about all inflection points

$\begingroup$

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?

$\endgroup$

1 Answer

$\begingroup$

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 $f(x) = x^4$.

$\endgroup$

Your Answer

Sign up or log in

Sign up using Google Sign up using Facebook Sign up using Email and Password Submit

Post as a guest

Post Your Answer Discard

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy