Find the absolute extrema if they exist, as well as all values of $x$ where they occur, for the function $f(x)=\frac{1}{3}{x}^3+\frac{1}{2}{x}^2-2x+5$ on the domain $-3,2.$

Find the derivative of $f(x)=\frac{1}{3}{x}^3+\frac{1}{2}{x}^2-2x+5$

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

Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.

A$.$ The absolute maximum is $,$ which occurs at $x=$

$($Round the absolute maximum to two decimal places as needed. Type an exact answer for the value of $x$ where the maximum occurs. Use a comma to separate answe

B$.$ There is no absolute maximum.