- The curve \(C\) has equation
$$y = ( x + 3 ) ( x - 1 ) ^ { 2 }$$
- Sketch \(C\) showing clearly the coordinates of the points where the curve meets the coordinate axes.
- Show that the equation of \(C\) can be written in the form
$$y = x ^ { 3 } + x ^ { 2 } - 5 x + k ,$$
where \(k\) is a positive integer, and state the value of \(k\).
There are two points on \(C\) where the gradient of the tangent to \(C\) is equal to 3 .
- Find the \(x\)-coordinates of these two points.