8. The curve \(C _ { 1 }\) has equation
$$y = x ^ { 2 } ( x + 2 )$$
- Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\)
- Sketch \(C _ { 1 }\), showing the coordinates of the points where \(C _ { 1 }\) meets the \(x\)-axis.
- Find the gradient of \(C _ { 1 }\) at each point where \(C _ { 1 }\) meets the \(x\)-axis.
The curve \(C _ { 2 }\) has equation
$$y = ( x - k ) ^ { 2 } ( x - k + 2 )$$
where \(k\) is a constant and \(k > 2\)
- Sketch \(C _ { 2 }\), showing the coordinates of the points where \(C _ { 2 }\) meets the \(x\) and \(y\) axes.