8.
\begin{figure}[h]
\captionsetup{labelformat=empty}
\caption{Figure 2}
\includegraphics[alt={},max width=\textwidth]{f01026a9-e5fe-4c19-b096-2bb4ad22c389-4_769_1150_269_379}
\end{figure}
Figure 2 shows part of the curve with equation
$$y = x ^ { 3 } - 6 x ^ { 2 } + 9 x .$$
The curve touches the \(x\)-axis at \(A\) and has a maximum turning point at \(B\).
- Show that the equation of the curve may be written as
$$y = x ( x - 3 ) ^ { 2 } ,$$
and hence write down the coordinates of \(A\).
- Find the coordinates of \(B\).
The shaded region \(R\) is bounded by the curve and the \(x\)-axis.
- Find the area of \(R\).