5 The equation of a curve is \(y = 6 x \mathrm { e } ^ { \frac { 1 } { 3 } x }\). At the point on the curve with \(x\)-coordinate \(p\), the gradient of the curve is 40 .
- Show that \(p = 3 \ln \left( \frac { 20 } { p + 3 } \right)\).
- Show by calculation that \(3.3 < p < 3.5\).
- Use an iterative formula based on the equation in part (i) to find the value of \(p\) correct to 3 decimal places. Give the result of each iteration to 5 decimal places.