Find the intervals on which $\backslash ($ f$($x$)\backslash )$ is increasing, the intervals on which $\backslash ($ f$($x$)\backslash )$ is decreasing, and the local extrema.

$\backslash [$

$\backslash$mathrm$\{$f$\}(\backslash$mathrm$\{$x$\})=(\backslash$mathrm$\{$x$\}-8)$ e$^\{-\backslash$mathrm$\{$x$\}\}$

$\backslash ]$

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

A$.$ The function is increasing on $\backslash ((-\backslash$infty$,9)\backslash ).$

$($Type your answer using interval notation. Type integers or simplified fractions. Use a comma to separate answers as needed.$)$

B$.$ The function is never increasing.

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

A$.$ The function is decreasing on $\backslash ((9,\backslash$infty$)\backslash ).$

$($Type your answer using interval notation. Type integers or simplified fractions. Use a comma to separate answers as needed.$)$

B$.$ The function is never decreasing.

Select the correct choice below and, if necessary, fill in the answer box to complete your choice. $($Type an integer or decimal rounded to four decimal places as needed. Use a comma to separate answers as needed.$)$

A$.$ The function has local maximum $\backslash (\backslash$mathrm$\{$f$\}(\backslash$mathrm$\{$c$\})=\backslash )$ and no local minimum.

B$.$ The function has local minimum $\backslash ($ f$($c$)=\backslash )$ and no local maximum.

C$.$ The function has local maximum $\backslash (\backslash$mathrm$\{$f$\}(\backslash$mathrm$\{$c$\})=\backslash )$ and local minimum $\backslash ($ f$($c$)=\backslash )$

D$.$ The function has no local extrema.