Let $f^{\text{'}}(x)=x^2+x-6.$

$($a$)(2$ points$)$ Find the interval$($s$)$ on which $f$ is increasing.

$($b$)(1$ point$)$ Identify the $x-$coordinates of any inflection points of $f.$

$($c$)(2$ points$)$ Find the absolute maximum value of $f^{\text{'}}$ on the interval $-1,3.$ Show your work.

$(3$ points$)$ Find the critical points of

$g(t)=\sqrt[3]{t^2}(2t-1)$ All please ;(