5
\includegraphics[max width=\textwidth, alt={}, center]{7b39a2ab-305d-43c5-a1e7-9442d6c13886-08_615_469_260_799} The diagram shows part of the curve with equation \(\mathrm { y } = \frac { \mathrm { x } ^ { 3 } } { \mathrm { x } + 2 }\). At the point \(P\), the gradient of the curve is 6 .

1. Show that the \(x\)-coordinate of \(P\) satisfies the equation \(x = \sqrt [ 3 ] { 12 x + 12 }\).
2. Show by calculation that the \(x\)-coordinate of \(P\) lies between 3.8 and 4.0 .
3. Use an iterative formula, based on the equation in part (a), to find the \(x\)-coordinate of \(P\) correct to 3 significant figures. Show the result of each iteration to 5 significant figures.