- The curve \(C\) has equation
$$y = x ^ { 2 } \cos \left( \frac { 1 } { 2 } x \right) \quad 0 < x \leqslant \pi$$
The curve has a stationary point at the point \(P\).
- Show, using calculus, that the \(x\) coordinate of \(P\) is a solution of the equation
$$x = 2 \arctan \left( \frac { 4 } { x } \right)$$
Using the iteration formula
$$x _ { n + 1 } = 2 \arctan \left( \frac { 4 } { x _ { n } } \right) \quad x _ { 1 } = 2$$
- find the value of \(x _ { 2 }\) and the value of \(x _ { 6 }\), giving your answers to 3 decimal places.