9. The curve \(C\) has equation \(y = \mathrm { f } ( x ) , x > 0\), and \(\mathrm { f } ^ { \prime } ( x ) = 4 x - 6 \sqrt { } x + \frac { 8 } { x ^ { 2 } }\).
Given that the point \(P ( 4,1 )\) lies on \(C\),
- find \(\mathrm { f } ( x )\) and simplify your answer.
- Find an equation of the normal to \(C\) at the point \(P ( 4,1 )\).