Find the intervals on which $g$ is increasing and decreasing.

$g(z)=sinz(z^2-2)+2zcoszon(0,2)$

Select the correct choice below and, if necessary, fill in the answer box$($es$)$ to complete your choice.

A$.$ The function $g$ is increasing on the open interval$($s$)$ and decreasing on the open interval$($s$)($Simplify your answer. Type an exact answer, using $$ as needed. Type your answer in interval notation. Use a comma to separate answers as needer

B$.$ The function $g$ is decreasing on the open interval$($s$)$ The function g is never increasing. $($Simplify your answer. Type an exact answer, using $$ as needed. Type your answer in interval notation. Use a comma to separate answers as needer

c$.$ The function g is increasing on the open interval$($s$)$ The function g is never decreasing.

$($Simplify your answer. Type an exact answer, using $$ as needed. Type your answer in interval notation. Use a comma to separate answers as needed

D$.$ The function $g$ is never increasing or decreasing.