Suppose the only critical values of $\displaystyle {f}'{\left({x}\right)},$ are at $\displaystyle {x}={10},{20}$, and $\displaystyle {30}$, and $\displaystyle {f}'{\left({x}\right)}$ and $\displaystyle {f}{''}{\left({x}\right)}$ have the following values:

$\displaystyle {x}$	$\displaystyle {5}$	$\displaystyle {10}$	$\displaystyle {15}$	$\displaystyle {20}$	$\displaystyle {25}$	$\displaystyle {30}$	$\displaystyle {35}$
$\displaystyle {f}'{\left({x}\right)}$	$\displaystyle -{4}$	$\displaystyle {0}$	$\displaystyle {3}$	$\displaystyle {0}$	$\displaystyle -{2}$	$\displaystyle {0}$	$\displaystyle {9}$
$\displaystyle {f}{''}{\left({x}\right)}$	$\displaystyle -{7}$	$\displaystyle {0}$	$\displaystyle {1}$	$\displaystyle -{7}$	$\displaystyle {5}$	$\displaystyle {8}$	$\displaystyle -{5}$

Based on this information,

At $\displaystyle {x}={10}$, you guarantee Select an answer there is a local maximum there is a local minimum nothing

At $\displaystyle {x}={20}$, you guarantee Select an answer there is a local maximum there is a local minimum nothing

At $\displaystyle {x}={30}$, you guarantee Select an answer there is a local maximum there is a local minimum nothing