5 The equation of a curve is \(y = x \ln ( 8 - x )\). The gradient of the curve is equal to 1 at only one point, when \(x = a\).
- Show that \(a\) satisfies the equation \(x = 8 - \frac { 8 } { \ln ( 8 - x ) }\).
- Verify by calculation that \(a\) lies between 2.9 and 3.1.
- Use an iterative formula based on the equation in part (i) to determine \(a\) correct to 2 decimal places. Give the result of each iteration to 4 decimal places.