\begin{enumerate}
\setcounter{enumi}{7}
\item \(f ( x ) = 2 + 6 x ^ { 2 } - x ^ { 3 }\).
- Find the coordinates of the stationary points of the curve \(y = \mathrm { f } ( x )\).
- Determine whether each stationary point is a maximum or minimum point.
- Sketch the curve \(y = \mathrm { f } ( x )\).
- State the set of values of \(k\) for which the equation \(\mathrm { f } ( x ) = k\) has three solutions.
\item The points \(P\) and \(Q\) have coordinates \(( 7,4 )\) and \(( 9,7 )\) respectively.