Given $f(x)=9-\frac{1}{2}{x}^2,$ find the following and simplify.

$($a$).f(xh)$

$($b$).f(xh)-f(x)$

$($c$).\frac{f(xh)-f(x)}{h}$

$($d$).$ If you let $h=0,$ what do you get from your answer to part $($c$)?$