Use the given function and its derivatives to answer the questions. Then sketch the graph.

f$($x$)=$ x$36$x$296$x $+58$

f$\text{'}($x$)=3($x $8)($x $+4)$

f$\text{'}\text{'}($x$)=6($x $2)$

$($a$)$ State the domain of

f$($x$).$

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

$($b$)$ State the y$-$intercept of

f$($x$).$

$($If an answer does not exist, enter DNE.$)$

$($x$,$ y$)=$

$($c$)$ State the open interval$($s$)$ where

f$($x$)$

is increasing. $($Enter your answer using interval notation. Enter EMPTY or $$ for the empty set.$)$

$($d$)$ State the open interval$($s$)$ where

f$($x$)$

is decreasing. $($Enter your answer using interval notation. Enter EMPTY or $$ for the empty set.$)$

$($e$)$ State any points where

f$($x$)$

has a local maximum. $($If an answer does not exist, enter DNE.$)$

$($x$,$ y$)=$

$($f$)$ State any points where

f$($x$)$

has a local minimum. $($If an answer does not exist, enter DNE.$)$

$($x$,$ y$)=$

$($g$)$ State the open interval$($s$)$ where

f$($x$)$

is concave up$.($Enter your answer using interval notation. Enter EMPTY or $$ for the empty set.$)$

$($h$)$ State the open interval$($s$)$ where

f$($x$)$

is concave down. $($Enter your answer using interval notation. Enter EMPTY or $$ for the empty set.$)$

$($i$)$ State any inflection points of

f$($x$).$

$($If an answer does not exist, enter DNE.$)$

$($x$,$ y$)=$

$($j$)$ State any vertical asymptotes of

f$($x$).$

$($Enter your answers as a comma$-$separated list of equations. If an answer does not exist, enter DNE.$)$

$($k$)$ State any horizontal asymptotes of

f$($x$).$

$($Enter your answers as a comma$-$separated list of equations. If an answer does not exist, enter DNE.$)$