The curve \(C\) has equation
$$y = \frac { x ^ { 2 } + \lambda x - 6 \lambda ^ { 2 } } { x + 3 }$$
where \(\lambda\) is a constant such that \(\lambda \neq 1\) and \(\lambda \neq - \frac { 3 } { 2 }\).
- Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) and deduce that if \(C\) has two stationary points then \(- \frac { 3 } { 2 } < \lambda < 1\).
- Find the equations of the asymptotes of \(C\).
- Draw a sketch of \(C\) for the case \(0 < \lambda < 1\).
- Draw a sketch of \(C\) for the case \(\lambda > 3\).