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

f$($x$)=2$x$^312$x$^2+9$

$($a$)$

Find the interval$($s$)$ of increase. $($Enter your answer using interval notation.$)$

Find the interval$($s$)$ of decrease. $($Enter your answer using interval notation.$)$

$($b$)$

Find the local minimum value$($s$).($Enter your answers as a comma$-$separated list.$)$

Find the local maximum value$($s$).($Enter your answers as a comma$-$separated list.$)$

$($c$)$

Find the inflection point.

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

Find the interval$($s$)$ where the function is concave up$.($Enter your answer using interval notation.$)$

Find the interval$($s$)$ where the function is concave down. $($Enter your answer using interval notation.$)$