Consider the function $f(x)=6x+2x^{-1}.$

$($a$)$ Find all critical numbers $c$ of $f.,c=$

$($b$)f$ is increasing for xin

$($c$)f$ is decreasing for xin

$($d$)f$ is concave up for xin

$($e$)f$ is concave down for xin

Note: Input U$,$ infinity, and $-$infinity for union, $,$ and $-,$ respectively. If there are multiple answers, separa none.