Suppose $\displaystyle {f{{\left({x}\right)}}}$ and $\displaystyle {f}'{\left({x}\right)}$ are continuous but restricted to the interval $\displaystyle {0}\le{x}\le{20}$, and assume the values of $\displaystyle {f}'{\left({x}\right)}$ are as shown. For each value, determine whether there is a local maximum, local minimum, or nothing.

$\displaystyle$$\displaystyle$

$\displaystyle {x}$	$\displaystyle {0}$	$\displaystyle {5}$	$\displaystyle {10}$	$\displaystyle {15}$	$\displaystyle {20}$
$\displaystyle {f}'{\left({x}\right)}$	$\displaystyle -{10}$	$\displaystyle {0}$	$\displaystyle -{6}$	$\displaystyle {3}$	$\displaystyle {4}$

At $\displaystyle {x}={0}$, you guarantee Select an answer there is a local maximum there is a local minimum nothing

At $\displaystyle {x}={5}$, you guarantee Select an answer there is a local maximum there is a local minimum nothing

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

At $\displaystyle {x}={15}$, 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