A function $f(x)$ has derivative $f^{\text{'}}(x)=-(x^2-2x)e^{-x}.$ On the open interval $(0,2)$ which of the following is true?

$($a$)f(x)$ is positive for all $x-$values in the interval.

$($b$)f(x)$ is decreasing for all $x-$values in the interval.

$($c$)f(x)$ is increasing for all $x-$values in the interval.

$($d$)f^{\text{'}}(x)$ is increasing for all $x-$values in the interval.

$($e$)f^{\text{'}}(x)$ is decreasing for all $x-$values in the interval.