By expanding the brackets, show that
$$( x - 4 ) ( x - 3 ) ( x + 1 ) = x ^ { 3 } - 6 x ^ { 2 } + 5 x + 12 .$$
Sketch the curve
$$y = x ^ { 3 } - 6 x ^ { 2 } + 5 x + 12$$
giving the coordinates of the points where the curve meets the axes. Label the curve \(C _ { 1 }\).
On the same diagram as in part (ii), sketch the curve
$$y = - x ^ { 3 } + 6 x ^ { 2 } - 5 x - 12$$
Label this curve \(C _ { 2 }\).