8 A curve \(y = \mathrm { f } ( x )\) has a stationary point at \(P ( 3 , - 10 )\). It is given that \(\mathrm { f } ^ { \prime } ( x ) = 2 x ^ { 2 } + k x - 12\), where \(k\) is a constant.
- Show that \(k = - 2\) and hence find the \(x\)-coordinate of the other stationary point, \(Q\).
- Find \(\mathrm { f } ^ { \prime \prime } ( x )\) and determine the nature of each of the stationary points \(P\) and \(Q\).
- Find \(\mathrm { f } ( x )\).