8 A curve has equation
$$y = x ^ { 3 } - 6 x + \frac { 9 } { x }$$
8
- Show that the \(x\) coordinates of the stationary points of the curve satisfy the equation
$$x ^ { 4 } - 2 x ^ { 2 } - 3 = 0$$
8
- Deduce that the curve has exactly two stationary points.
8 - Find the coordinates and nature of the two stationary points.
Fully justify your answer.
[0pt]
[4 marks]
8 - Write down the equation of a line which is a tangent to the curve in two places.