Find the interval$($s$)$ where the function is increasing and the interval$($s$)$ where it is decreasing. $($Enter your answer using interval notation. If an answer does not exist, enter DNE.$)$

Complete the following parts.

$($a$)$ The domain of the function $f$ is $-($Enter your answer using interval notation.$)$

$($b$)$ To determine the interval$($s$)$ where the function is increasing and the interval$($s$)$ where it is decreasing, we use the $---$Select$---$

$($c$)$ To determine the interval$($s$)$ where the function is increasing and the interval$($s$)$ where it is decreasing, we need the critical numbers of $---$ Select$---$ hat$(0).$

$($d$)$ To find these critical numbers, we need to find $-($Factor your answer completely.$)$

$($e$)$ These critical numbers are as follows. $($Enter your answers as a comma$-$separated list. If an answer does not exist, enter DNE.$)$

$x=$

$($f$)$ Then, we use these critical numbers to construct the sign diagram for $0.$