- The curve \(C _ { 1 }\) has equation
$$y = \frac { 6 } { x } + 3$$
- Sketch \(C _ { 1 }\) stating the coordinates of any points where the curve cuts the coordinate axes.
- State the equations of any asymptotes to the curve \(C _ { 1 }\)
The curve \(C _ { 2 }\) has equation
$$y = 3 x ^ { 2 } - 4 x - 10$$
- Show that \(C _ { 1 }\) and \(C _ { 2 }\) intersect when
$$3 x ^ { 3 } - 4 x ^ { 2 } - 13 x - 6 = 0$$
Given that the \(x\) coordinate of one of the points of intersection is \(- \frac { 2 } { 3 }\)
- use algebra to find the \(x\) coordinates of the other points of intersection between \(C _ { 1 }\) and \(C _ { 2 }\)
(Solutions relying on calculator technology are not acceptable.)