- The curve \(C\) has equation
$$( x + y ) ^ { 3 } = 3 x ^ { 2 } - 3 y - 2$$
- Find an expression for \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) in terms of \(x\) and \(y\).
The point \(P ( 1,0 )\) lies on \(C\).
- Show that the normal to \(C\) at \(P\) has equation
$$y = - 2 x + 2$$
- Prove that the normal to \(C\) at \(P\) does not meet \(C\) again.
You should use algebra for your proof and make your reasoning clear.