Suppose that

$\backslash [$

f$($x$)=5$ x$^\{2\}-$x$^\{3\}+2$

$\backslash ]$

$($A$)$ Find all critical numbers of $\backslash ($ f $\backslash ).$ If there are no critical numbers, enter 'NONE'.

Critical numbers $=$

$($B$)$ Use interval notation to indicate where $\backslash ($ f$($x$)\backslash )$ is increasing.

Note: Use 'INF' for $\backslash (\backslash$infty $\backslash ),\text{'}-$INF' for $\backslash (-\backslash$infty $\backslash ),$ and use $\text{'}$U$\text{'}$ for the union symbol.

Increasing:

$($C$)$ Use interval notation to indicate where $\backslash ($ f$($x$)\backslash )$ is decreasing.

Decreasing:

$($D$)$ List the $\backslash ($ x $\backslash )-$coordinates of all local maxima of $\backslash ($ f $\backslash ).$ If there are no local maxima, enter 'NONE'.

$\backslash ($ x $\backslash )$ values of local maxima $\backslash (=\backslash )$

$($E$)$ List the $\backslash ($ x $\backslash )-$coordinates of all local minima of $\backslash ($ f $\backslash ).$ If there are no local minima, enter 'NONE'.

$\backslash ($ x $\backslash )$ values of local minima $\backslash (=\backslash )$

$($F$)$ Use interval notation to indicate where $\backslash ($ f$($x$)\backslash )$ is concave up$.$

Concave up:

$($G$)$ Use interval notation to indicate where $\backslash ($ f$($x$)\backslash )$ is concave down.

Concave down:

$($H$)$List the $\backslash ($ x $\backslash )$ values of all inflection points of $\backslash ($ f $\backslash ).$ If there are no inflection points, enter 'NONE'.

$\backslash ($ x $\backslash )$ values of inflection points $\backslash (=\backslash )$