Consider the function $f(x) = 12 x^5 + 30 x^4 - 160 x^3 + 2$. For this function there are four important intervals: $(-\infty, A]$, $[A,B]$,$[B,C]$, and $[C,\infty)$ where $A$, $B$, and $C$ are the critical numbers.
Find $A$
and $B$
and $C$
At each critical number $A$, $B$, and $C$ does $f(x)$ have a local min, a local max, or neither? Type in your answer as LMIN, LMAX, or NEITHER.
At $A$
At $B$
At $C$