10 A curve has equation \(y = \mathrm { f } ( x )\) and it is given that \(\mathrm { f } ^ { \prime } ( x ) = a x ^ { 2 } + b x\), where \(a\) and \(b\) are positive constants.
- Find, in terms of \(a\) and \(b\), the non-zero value of \(x\) for which the curve has a stationary point and determine, showing all necessary working, the nature of the stationary point.
- It is now given that the curve has a stationary point at \(( - 2 , - 3 )\) and that the gradient of the curve at \(x = 1\) is 9 . Find \(\mathrm { f } ( x )\).