13.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{deba6a2b-1821-4110-bde8-bde18a5f9be9-32_800_787_244_644}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{figure}
Figure 3 shows a sketch of part of the curve with equation
$$y = 2 x ^ { 3 } - 17 x ^ { 2 } + 40 x$$
The curve has a minimum turning point at \(x = k\).
The region \(R\), shown shaded in Figure 3, is bounded by the curve, the \(x\)-axis and the line with equation \(x = k\).
Show that the area of \(R\) is \(\frac { 256 } { 3 }\)
(Solutions based entirely on graphical or numerical methods are not acceptable.)