- The curve \(C\) has equation \(y = \mathrm { f } ( x ) , x > 0\), where
$$f ^ { \prime } ( x ) = 3 \sqrt { x } - \frac { 9 } { \sqrt { x } } + 2$$
Given that the point \(P ( 9,14 )\) lies on \(C\),
- find \(\mathrm { f } ( x )\), simplifying your answer,
- find an equation of the normal to \(C\) at the point \(P\), giving your answer in the form \(a x + b y + c = 0\) where \(a , b\) and \(c\) are integers.