- The curve \(C _ { 1 }\) has equation
$$y = x \left( 4 - x ^ { 2 } \right)$$
- Sketch the graph of \(C _ { 1 }\) showing the coordinates of any points of intersection with the coordinate axes.
The curve \(C _ { 2 }\) has equation \(y = \frac { A } { x }\) where \(A\) is a constant.
- Show that the \(x\) coordinates of the points of intersection of \(C _ { 1 }\) and \(C _ { 2 }\) satisfy the equation
$$x ^ { 4 } - 4 x ^ { 2 } + A = 0$$
- Hence find the range of possible values of \(A\) for which \(C _ { 1 }\) meets \(C _ { 2 }\) at 4 distinct points.