Consider the function $f(x) = -2 x^3 + 30 x^2 - 96 x + 3$. For this function there are three important intervals: $(-\infty, A]$, $[A,B]$, and $[B,\infty)$ where $A$ and $B$ are the critical values.
Find $A$
and $B$
For each of the following intervals, tell whether $f(x)$ is increasing (type in INC) or decreasing (type in DEC).
$(-\infty, A]$:
$[A,B]$:
$[B,\infty)$
$f(x)$ has an inflection point at $x =C$
where $C$ is
Finally for each of the following intervals, tell whether $f(x)$ is concave up (type in CU) or concave down (type in CD).
$(-\infty, C]$:
$[C,\infty)$