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

f$($x$)=$ x$^327$x $+4$

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

Find the interval 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.

Find the interval where the graph is concave upward. $($Enter your answer using interval notation.$)$

Find the interval where the graph is concave downward. $($Enter your answer using interval notation.$)$

$($d$)$ Use the information from parts $($a$)($c$)$ to sketch the graph. Check your work with a graphing device if you have one.

The x$$y$-$coordinate plane is given. The curve enters the window in the third quadrant, goes down and right becoming less steep, changes direction at the point $(3,58),$ goes up and right becoming more steep, passes through the point $(0,4),$ goes up and right becoming less steep, crosses the x$-$axis at approximately x $=0\mathrm{.}1,$ changes direction at the point $(3,50),$ goes down and right becoming more steep, and exits the window in the first quadrant.

The x$$y$-$coordinate plane is given. The curve enters the window in the second quadrant, goes up and right becoming less steep, changes direction at the point $(3,58),$ goes down and right becoming more steep, passes through the point $(0,4),$ goes down and right becoming less steep, crosses the x$-$axis at approximately x $=0\mathrm{.}1,$ changes direction at the point $(3,50),$ goes up and right becoming more steep, and exits the window in the fourth quadrant.

The x$$y$-$coordinate plane is given. The curve enters the window in the second quadrant, goes down and right becoming less steep, crosses the x$-$axis at approximately x $=3\mathrm{.}2,$ changes direction at the approximate point $(1\mathrm{.}7,14),$ goes up and right becoming more steep, passes through the point $(0,4),$ goes up and right becoming less steep, crosses the x$-$axis at approximately x $=0\mathrm{.}5,$ changes direction at the approximate point $(1\mathrm{.}7,6),$ goes down and right becoming more steep, crosses the x$-$axis at approximately x $=2\mathrm{.}7,$ and exits the window in the fourth quadrant.

The x$$y$-$coordinate plane is given. The curve enters the window in the third quadrant, goes up and right becoming less steep, crosses the x$-$axis at approximately x $=3\mathrm{.}2,$ changes direction at the approximate point $(1\mathrm{.}7,14),$ goes down and right becoming more steep, passes through the point $(0,4),$ goes down and right becoming less steep, crosses the x$-$axis at approximately x $=0\mathrm{.}5,$ changes direction at the approximate point $(1\mathrm{.}7,6),$ goes up and right becoming more steep, crosses the x$-$axis at approximately x $=2\mathrm{.}7,$ and exits the window in the first quadrant.