15. A curve has equation \(y = \mathrm { g } ( x )\).
Given that
- \(\mathrm { g } ( x )\) is a cubic expression in which the coefficient of \(x ^ { 3 }\) is equal to the coefficient of \(x\)
- the curve with equation \(y = \mathrm { g } ( x )\) passes through the origin
- the curve with equation \(y = \mathrm { g } ( x )\) has a stationary point at \(( 2,9 )\)
- find \(g ( x )\),
- prove that the stationary point at \(( 2,9 )\) is a maximum.
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