15.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{a75c9ef7-b648-47be-bad1-fc8b315be3df-22_796_974_244_548}
\captionsetup{labelformat=empty}
\caption{Figure 4}
\end{figure}
Figure 4 shows a sketch of the curve \(C\) with equation
$$y = 5 x ^ { \frac { 3 } { 2 } } - 9 x + 11 , x \geqslant 0$$
The point \(P\) with coordinates \(( 4,15 )\) lies on \(C\).
The line \(l\) is the tangent to \(C\) at the point \(P\).
The region \(R\), shown shaded in Figure 4, is bounded by the curve \(C\), the line \(l\) and the \(y\)-axis.
Show that the area of \(R\) is 24 , making your method clear.
(Solutions based entirely on graphical or numerical methods are not acceptable.)