4 The gradient of the curve \(y = \left( 2 x ^ { 2 } + 9 \right) ^ { \frac { 5 } { 2 } }\) at the point \(P\) is 100 .
- Show that the \(x\)-coordinate of \(P\) satisfies the equation \(x = 10 \left( 2 x ^ { 2 } + 9 \right) ^ { - \frac { 3 } { 2 } }\).
- Show by calculation that the \(x\)-coordinate of \(P\) lies between 0.3 and 0.4 .
- Use an iterative formula, based on the equation in part (i), to find the \(x\)-coordinate of \(P\) correct to 4 decimal places. You should show the result of each iteration.