IMathAS-libretexts

For all of the matches below,

\displaystyle {x}={c}

is a critical number of

\displaystyle {f}

$\displaystyle {f}$ is concave up and has a local minimum at $\displaystyle {x}={c}$ .
$\displaystyle {f}$ may have a local maximum, a local minimum, or neither at $\displaystyle {x}={c}$ .
$\displaystyle {f}$ is concave down and has a local maximum at $\displaystyle {x}={c}$ .