$(1$ point$)$ Answer the following questions for the function

$f(x)=\frac{x^3}{x^2-9}.$

Enter "INF" for $$ and $"-$INF" for $-.$

A$.$ The function $f(x)$ has two vertical asympototes:

$x=$

B$.f(x)$ has one local maximum and one local minimum occuring at $x$ values :

$x_{\text{m}\text{a}\text{x}}=,$ and $x_{\text{m}\text{i}\text{n}}=$

C$.$ For each interval, tell whether $f(x)$ is increasing $($type in INC$)$ or decreasing $($type in DEC$).$

$(-,$max$)$

$(max,-3)$

$(-3,0)$

$(0,3)$

$(3,$min$)$

$(min,+)$

D$.f(x)$ is concave up on the open intervals:

E$.$ The inflection point for this function occurs at $x=$

F$.$ Sketch the graph of $f(x)$ and bring it to class.