8 The curve with equation \(y = \frac { x ^ { 3 } } { \mathrm { e } ^ { x } - 1 }\) has a stationary point at \(x = p\), where \(p > 0\).
- Show that \(p = 3 \left( 1 - \mathrm { e } ^ { - p } \right)\).
- Verify by calculation that \(p\) lies between 2.5 and 3 .
- Use an iterative formula based on the equation in part (a) to determine \(p\) correct to 2 decimal places. Give the result of each iteration to 4 decimal places.