6
\includegraphics[max width=\textwidth, alt={}, center]{89e54367-bb83-483a-add5-0527b71a5cac-4_476_709_251_683} The diagram shows the curve with equation \(x = \ln \left( y ^ { 3 } + 2 y \right)\). At the point \(P\) on the curve, the gradient is 4 and it is given that \(P\) is close to the point with coordinates (7.5,12).

1. Find \(\frac { \mathrm { d } x } { \mathrm {~d} y }\) in terms of \(y\).
2. Show that the \(y\)-coordinate of \(P\) satisfies the equation $$y = \frac { 12 y ^ { 2 } + 8 } { y ^ { 2 } + 2 }$$
3. By first using an iterative process based on the equation in part (ii), find the coordinates of \(P\), giving each coordinate correct to 3 decimal places.