Suppose that

$f(x)=9x^{2}ln(x),x>0.$

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

critical numbers $=$

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

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

Increasing:

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

Decreasing:

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

$x$ values of local maxima $=$

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

$x$ values of local minima $=$

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

Concave up:

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

Concave down:

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

$x$ values of inflection points $=$

$($I$)$ Use all of the preceding information to sketch a graph of $f.$ When you're finished, enter a $"1"$ in the box below.

Graph Complete: