6. In this question you must show all stages of your working.
\section*{Solutions relying on calculator technology are not acceptable.}
A curve \(C\) has equation \(y = \mathrm { f } ( x )\) where
$$f ( x ) = 2 ( x + 1 ) ( x - 3 ) ^ { 2 }$$
- Sketch a graph of \(C\).
Show on your graph the coordinates of the points where \(C\) cuts or meets the coordinate axes.
- Write \(\mathrm { f } ( x )\) in the form \(a x ^ { 3 } + b x ^ { 2 } + c x + d\), where \(a , b , c\) and \(d\) are constants to be found.
- Hence, find the equation of the tangent to \(C\) at the point where \(x = \frac { 1 } { 3 }\)