For $f(x)=x^3-\frac{1}{2}{x}^2-6x+2,$ find

$($a$)$ The domain and the $y$ intercept.

Domain all real #$\text{'}$s

$y-$int:

$($b$)$ The intervals where the function is increasing and decreasing.

$($c$)$ The Relative Maximum and Minimum.

$($d$)$ The points of inflection.

$($e$)$ Concavity.