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\includegraphics[max width=\textwidth, alt={}, center]{873a104f-e2e2-49bb-b943-583769728fbb-06_355_839_260_653} The diagram shows the curve with equation \(y = \frac { 5 \ln x } { 2 x + 1 }\). The curve crosses the \(x\)-axis at the point \(P\) and has a maximum point \(M\).

1. Find the gradient of the curve at the point \(P\).
2. Show that the \(x\)-coordinate of the point \(M\) satisfies the equation \(x = \frac { x + 0.5 } { \ln x }\).
3. Use an iterative formula based on the equation in part (ii) to find the \(x\)-coordinate of \(M\) correct to 4 significant figures. Show the result of each iteration to 6 significant figures.