Suppose $\displaystyle {f}'{\left({x}\right)}$ is continuous for all $\displaystyle {x}$, and $\displaystyle {f{{\left({x}\right)}}}$ has a local extreme value $\displaystyle {x}={7}$.

Complete the following table with appropriate possibilities for the values of $\displaystyle {f}'{\left({x}\right)}$ at $\displaystyle {x}={5},{7},{12}$..

$\displaystyle {x}$	$\displaystyle {5}$	$\displaystyle {7}$	$\displaystyle {12}$
$\displaystyle {f}'{\left({x}\right)}$

Based on your table, $\displaystyle {f{{\left({x}\right)}}}$ is Select an answer increasing decreasing until $\displaystyle {x}={7}$, and is Select an answer increasing decreasing after.

The function $\displaystyle {f{{\left({x}\right)}}}$ will have a Select an answer neither a maximum nor a minimum local maximum local minimum at $\displaystyle {x}={7}$.