Answer the following questions for the function $$f(x) = \frac{ x^3 }{ x^2 - 4 }.$$

Enter points, such as inflection points in ascending order, i.e. smallest $x$ values first. Enter "INF" for $\infty$ and "MINF" for $- \infty$.

Enter intervals in ascending order also.

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

B. $f(x)$ has one local maximum and one local minimum:
$max =$ and $min =$

C. For each interval, tell whether $f(x)$ is increasing (type in INC) or decreasing (type in DEC).
$(- \infty, max)$
$(max, -2)$
$(-2, 0)$
$(0,2)$
$(2, min)$
$(min, + \infty)$

D. $f(x)$ is concave up on the interval (, )
and on the inteval (, )

E. The inflection point for this function is

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