$[20]2.$ For $f(x)=x^3-6x^2+9x+20,$ on domain $0,4$ :

$($a$)$ Calculate its average rate of change of $f$ between $x=0$ and $x=2.$

$($b$)$ Calculate its derivative $f^{\text{'}}.$

$($c$)$ Find its critical points and the interval$($s$)$ on which $f$ is increasing$/$decreasing$.$

$($d$)$ Calculate its second derivative $f^{\text{'}\text{'}}.$

$($e$)$ Classify each critical point as a local minimum, local maximum, or neither.

$($f$)$ Find any points of inflection.

$($g$)$ Find the absolute maximum and minimum values of the function on its domain $0,4.$