4. The curve \(C\) has equation
$$4 x ^ { 2 } - y ^ { 3 } - 4 x y + 2 ^ { y } = 0$$
The point \(P\) with coordinates \(( - 2,4 )\) lies on \(C\).
- Find the exact value of \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) at the point \(P\).
The normal to \(C\) at \(P\) meets the \(y\)-axis at the point \(A\).
- Find the \(y\) coordinate of \(A\), giving your answer in the form \(p + q \ln 2\), where \(p\) and \(q\) are constants to be determined.
(3)