4 A curve has parametric equations
$$x = t ^ { 2 } + 3 t + 1 , \quad y = t ^ { 4 } + 1$$
The point \(P\) on the curve has parameter \(p\). It is given that the gradient of the curve at \(P\) is 4 .
- Show that \(p = \sqrt [ 3 ] { } ( 2 p + 3 )\).
- Verify by calculation that the value of \(p\) lies between 1.8 and 2.0.
- Use an iterative formula based on the equation in part (i) to find the value of \(p\) correct to 2 decimal places. Give the result of each iteration to 4 decimal places.