IMathAS-libretexts

Suppose that

\displaystyle {f}

is a function with

\displaystyle {f}'{\left({4}\right)}={0}

and

\displaystyle {f}{''}{\left({4}\right)}={0}

Then $\displaystyle {f}$ has a relative maximum at $\displaystyle {x}={4}$ .
Then $\displaystyle {f}$ has a relative minimum at $\displaystyle {x}={4}$ .
Given this information, we cannot determine whether $\displaystyle {f}$ has a maximum or a minimum at $\displaystyle {x}={4}$ .