9.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{8daf56fa-bfce-454e-bbb8-fecd8170d77e-28_751_876_214_539}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{figure}
Figure 3 shows a sketch of part of the curve with equation
$$y = 7 x ^ { 2 } ( 5 - 2 \sqrt { x } ) , \quad x \geqslant 0$$
The curve has a turning point at the point \(A\), where \(x > 0\), as shown in Figure 3.
- Using calculus, find the coordinates of the point \(A\).
The curve crosses the \(x\)-axis at the point \(B\), as shown in Figure 3.
- Use algebra to find the \(x\) coordinate of the point \(B\).
The finite region \(R\), shown shaded in Figure 3, is bounded by the curve, the line through \(A\) parallel to the \(x\)-axis and the line through \(B\) parallel to the \(y\)-axis.
- Use integration to find the area of the region \(R\), giving your answer to 2 decimal places.