- The curve \(C\) has equation \(y = \mathrm { f } ( x )\), where
$$f ^ { \prime } ( x ) = ( x - 3 ) ( 3 x + 5 )$$
Given that the point \(P ( 1,20 )\) lies on \(C\),
- find \(\mathrm { f } ( x )\), simplifying each term.
- Show that
$$f ( x ) = ( x - 3 ) ^ { 2 } ( x + A )$$
where \(A\) is a constant to be found.
- Sketch the graph of \(C\). Show clearly the coordinates of the points where \(C\) cuts or meets the \(x\)-axis and where \(C\) cuts the \(y\)-axis.