please consider the function f$($x$)=8$x $2$ ln$($x$).($a$)$ What is the domain of f$?($b$)$ Does f have any x$-$intercepts? Please list them if any. $($c$)$ Does f have any y$-$intercepts? Please list them if any. $($d$)$ Please compute f $,$ make a sign chart, and use it to determine the interval$($s$)$ where f is increasing, and the interval$($s$)$ where f is decreasing. $($e$)$ Please compute f $,$ make a sign chart, and use it to determine the interval$($s$)$ where f is concave up$,$ and the interval$($s$)$ where f is concave down. $($f$)$ Use the fact that lim x$0+$ f$($x$)=0$ and the information you have found above to sketch the graph of f$.$ Please label your axes, and the intercepts, extrema $($maxima and minima$),$ and inflection points. When you are done, please double$-$check that your graph has the correct domain $($which you found in part $($a$))$