$($a$)$ On what intervals is $f$ increasing or decreasing? $($Enter your answers using interval notation.$)$

increasing

decreasing $$

$($b$)$ At what values of $x$ does $f$ have a local maximum or minimum? $($Enter your answers as a comma$-$separated list. If an answer does not exist, enter DNE.$)$

local maximum $,x=$

local minimum $,x=$

$($c$)$ If it is known that $f(0)=0,$ sketch a possible araph of $f$

$($senders note: dont ask for more info it is all in the picture$)$