9.
\begin{figure}[h]
\captionsetup{labelformat=empty}
\caption{Figure 2}
\includegraphics[alt={},max width=\textwidth]{815e288c-0140-4c12-9e89-b0bb4fb1a8c1-12_812_1088_317_427}
\end{figure}
Figure 2 shows part of the curve \(C\) with equation
$$y = ( x - 1 ) \left( x ^ { 2 } - 4 \right) .$$
The curve cuts the \(x\)-axis at the points \(P , ( 1,0 )\) and \(Q\), as shown in Figure 2.
- Write down the \(x\)-coordinate of \(P\), and the \(x\)-coordinate of \(Q\).
- Show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = 3 x ^ { 2 } - 2 x - 4\).
- Show that \(y = x + 7\) is an equation of the tangent to \(C\) at the point ( \(- 1,6\) ).
The tangent to \(C\) at the point \(R\) is parallel to the tangent at the point ( \(- 1,6\) ).
- Find the exact coordinates of \(R\).