6 The curve with equation \(y = x ^ { 2 } \cos \frac { 1 } { 2 } x\) has a stationary point at \(x = p\) in the interval \(0 < x < \pi\).
- Show that \(p\) satisfies the equation \(\tan \frac { 1 } { 2 } p = \frac { 4 } { p }\).
- Verify by calculation that \(p\) lies between 2 and 2.5.
- Use the iterative formula \(p _ { n + 1 } = 2 \tan ^ { - 1 } \left( \frac { 4 } { p _ { n } } \right)\) to determine the value of \(p\) correct to 2 decimal places. Give the result of each iteration to 4 decimal places.