$1.$ For this problem, 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 limx$0+$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.