8 The equation of a curve is \(y = \ln x + \frac { 2 } { x }\), where \(x > 0\).
- Find the coordinates of the stationary point of the curve and determine whether it is a maximum or a minimum point.
- The sequence of values given by the iterative formula
$$x _ { n + 1 } = \frac { 2 } { 3 - \ln x _ { n } }$$
with initial value \(x _ { 1 } = 1\), converges to \(\alpha\). State an equation satisfied by \(\alpha\), and hence show that \(\alpha\) is the \(x\)-coordinate of a point on the curve where \(y = 3\).
- Use this iterative formula to find \(\alpha\) correct to 2 decimal places, showing the result of each iteration.