Consider the function $f(x) = 3 x + 6 x ^ { -1 }$. For this function there are four important intervals: $(-\infty, A]$, $[A,B)$,$(B,C]$, and $[C,\infty)$ where $A$, and $C$ are the critical numbers and the function is not defined at $B$.
Find $A$
and $B$
and $C$
For each of the following intervals, tell whether $f(x)$ is increasing (type in INC) or decreasing (type in DEC).
$(-\infty, A]$:
$[A,B)$:
$(B,C]$:
$[C,\infty)$
Note that this function has no inflection points, but we can still consider its concavity. For each of the following intervals, tell whether $f(x)$ is concave up (type in CU) or concave down (type in CD).
$(-\infty, B)$:
$(B,\infty)$: