9. A curve with equation \(y = \mathrm { f } ( x )\) passes through the point ( 3,6 ). Given that
$$f ^ { \prime } ( x ) = ( x - 2 ) ( 3 x + 4 )$$
- use integration to find \(\mathrm { f } ( x )\). Give your answer as a polynomial in its simplest form.
- Show that \(\mathrm { f } ( x ) \equiv ( x - 2 ) ^ { 2 } ( x + p )\), where \(p\) is a positive constant. State the value of \(p\).
- Sketch the graph of \(y = \mathrm { f } ( x )\), showing the coordinates of any points where the curve touches or crosses the coordinate axes.