7 The curve with equation \(\mathrm { e } ^ { 2 x } - 18 x + y ^ { 3 } + y = 11\) has a stationary point at \(( p , q )\).
- Find the exact value of \(p\).
- Show that \(q = \sqrt [ 3 ] { 2 + 18 \ln 3 - q }\).
- Show by calculation that the value of \(q\) lies between 2.5 and 3.0.
- Use an iterative formula, based on the equation in (b), to find the value of \(q\) correct to 4 significant figures. Give the result of each iteration to 6 significant figures.
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