- (a) Factorise completely \(9 x - x ^ { 3 }\)
The curve \(C\) has equation
$$y = 9 x - x ^ { 3 }$$
(b) Sketch \(C\) showing the coordinates of the points at which the curve cuts the \(x\)-axis.
The line \(l\) has equation \(y = k\) where \(k\) is a constant.
Given that \(C\) and \(l\) intersect at 3 distinct points,
(c) find the range of values for \(k\), writing your answer in set notation.
Solutions relying on calculator technology are not acceptable.