$(1$ point$)$ Suppose $f(x)=\sqrt[3]{x}{e}^{-x}.$

Find the intervals $on$ which $fis$ increasing $or$ decreasing.

$fis$ increasing $on$

$fis$ decreasing $on$

$(Enter$ your answer using interval notation.$)$

Find the local maximum and minimum values $off.$

Local maximum values are

$0\mathrm{.}496815062611573$

Local minimum values are

$n$

$(If$ there are none, enter "none". $If$ there $is$ more than one, enter a comma$-$separated list.$)$

Find the intervals $of$ concavity.

$fis$ concave $upon$

$fis$ concave down $on(0,0\mathrm{.}244017)(0\mathrm{.}244017,0\mathrm{.}910684)$

$(Enter$ your answer using interval notation.$)$

Use your answers above $to$ sketch the graph $ofy=f(x).$