EXAMPLE $7$ Sketch a graph of the function $\backslash [$ f$($x$)=$x$^\{5\}-4$ x$^\{3\}\backslash ]$ using the following steps. $($a$)$ Identify where the extrema of $\backslash ($ f $\backslash )$ occur. $($b$)$ Find the intervals on which $\backslash ($ f $\backslash )$ is increasing and the intervals on which $\backslash ($ f $\backslash )$ is decreasing. $($c$)$ Find where the graph of $\backslash ($ f $\backslash )$ is concave up and where it is concave down. $($d$)$ Sketch the general shape of the graph for $\backslash ($ f $\backslash ).($e$)$ Plot some specific points, such as local maximum and minimum points, points of inflection, and intercepts. Then sketch the curve.