14 The equation of a curve is
\(y = x ^ { 2 } ( x - 2 ) ^ { 3 }\).
- Find \(\frac { \mathrm { dy } } { \mathrm { dx } }\), giving your answer in factorised form.
- Determine the coordinates of the stationary points on the curve.
In part (c) you may use the result \(\frac { d ^ { 2 } y } { d x ^ { 2 } } = 4 ( x - 2 ) \left( 5 x ^ { 2 } - 8 x + 2 \right)\).
- Determine the nature of the stationary points on the curve.
- Sketch the curve.