6 The equation of a curve is \(y = \frac { 3 x ^ { 2 } } { x ^ { 2 } + 4 }\). At the point on the curve with positive \(x\)-coordinate \(p\), the gradient of the curve is \(\frac { 1 } { 2 }\).
- Show that \(p = \sqrt { } \left( \frac { 48 p - 16 } { p ^ { 2 } + 8 } \right)\).
- Show by calculation that \(2 < p < 3\).
- Use an iterative formula based on the equation in part (i) to find the value of \(p\) correct to 4 significant figures. Give the result of each iteration to 6 significant figures.