$f(x)=x^3-4\mathrm{.}5x^2-12x+2$

a$)$ Determine the intervals on which $f$ is concave up and concave down.

$f$ is concave up on: $$

$f$ is concave down on:

b$)$ Based on your answer to part $($a$),$ determine the inflection points of $f.$ Each point should be entered as an ordered pair $($that is$,$ in the form $(x,y)).$

$($Separate multiple answers by commas.$)$

c$)$ Find the critical numbers of $f$ and use the Second Derivative Test, when possible, to determine the relative extrema. List only the $x-$coordinates.

Relative maxima at: $($Separate multiple answers by commas.$)$

Relative minima at: $($Separate multiple answers by commas.$)$

d$)$ Find the $x-$value$($s$)$ where $f^{\text{'}}(x)$ has a relative maximum or minimum.

$f^{\text{'}}$ has relative maxima at: $($Separate multiple answers by commas.$)$

$f^{\text{'}}$ has relative minima at: $($Separate multiple answers by commas.$)$