5 The curve with equation \(y = x \ln ( 4 x + 1 ) - 3 x\) has one stationary point \(P\).
- Show that the \(x\)-coordinate of \(P\) satisfies the equation
$$x = \frac { 2 x + 0.75 } { \ln ( 4 x + 1 ) } - 0.25$$
- Show by calculation that the \(x\)-coordinate of \(P\) lies between 1.8 and 1.9.
- Use an iterative formula, based on the equation in part (a), to find the \(x\)-coordinate of \(P\) correct to 3 significant figures. Give the result of each iteration to 5 significant figures.