I have a conjecture on local max/min , can any of you propose a contradiction? If $f$ is a non-piecewise function defined continuous on an interval $I$, and within that interval $I$, there exists a value $x$, such that $f`(x)$ (derivative of $f$) does not exist , then at that value $x$, is a local $\max/\min$ value.

I'm surprised no one has said $$f(x)=\sqrt[3] x$$ The derivative at $x=0$ is undefined (or $\infty$ if you like) but that is not an extremum of the function.
