$8.[7$ marks$].$ For the function given by $\backslash ($ f$($x$)=\backslash$frac$\{$x$^\{3\}\}\{1-$x$\}\backslash )$ :

$($i$)$ Determine the function's domain $\backslash (($D$($f$))\backslash )$ and determine whether the function is odd, even or neither;

$($ii$)$ Determine the sign of the function $($i$.$e$.$ where it is positive or negative$)$;

$($iii$)$ Determine the limiting behaviour at the domain boundaries;

$($iv$)$ Determine the derivative and, by examining its sign, state the intervals over which the function is increasing or decreasing;

$($v$)$ Determine the positions and forms of the stationary points, if any;

$($vi$)$ Determine the concavity of the function and, if any, note any points of inflection;

$($vii$)$ Provide a qualitative sketch the function, clearly labelling important points.