Express \(3 x ^ { 2 } - 6 x + 2\) in the form \(a ( x + b ) ^ { 2 } + c\), where \(a , b\) and \(c\) are constants.
The function f , where \(\mathrm { f } ( x ) = x ^ { 3 } - 3 x ^ { 2 } + 7 x - 8\), is defined for \(x \in \mathbb { R }\). Find \(\mathrm { f } ^ { \prime } ( x )\) and state, with a reason, whether f is an increasing function, a decreasing function or neither.