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

f$($x$)=$ x$312$x$227$x $+2$

$($a$)$

Find the interval$($s$)$ on which f is increasing. $($Enter your answer using interval notation.$)$

$($$,1)(9,$$)$

Find the interval$($s$)$ on which f is decreasing. $($Enter your answer using interval notation.$)$

$(1,9)$

$($b$)$

Find the local minimum and maximum values of f$.$

local minimum value$$

$478$

local maximum value$$

$22$

$($c$)$

Find the inflection point.

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

$4,228$

Find the interval$($s$)$ on which f is concave up$.($Enter your answer using interval notation.$)$

$(4,$$)$

Find the interval$($s$)$ on which f is concave down. $($Enter your answer using interval notation.$)$

$($$,4)$