9 The equation of a curve is \(y = x ^ { 3 } + p x ^ { 2 }\), where \(p\) is a positive constant.
- Show that the origin is a stationary point on the curve and find the coordinates of the other stationary point in terms of \(p\).
- Find the nature of each of the stationary points.
Another curve has equation \(y = x ^ { 3 } + p x ^ { 2 } + p x\).
- Find the set of values of \(p\) for which this curve has no stationary points.
[0pt]
[Question 10 is printed on the next page.]