- In this question you must show all stages of your working.
The curve \(C\) has equation \(y = \mathrm { f } ( x ) , x > 0\)
Given that
- the point \(P ( 2,8 \sqrt { 2 } )\) lies on \(C\)
- \(\mathrm { f } ^ { \prime } ( x ) = 4 \sqrt { x ^ { 3 } } + \frac { k } { x ^ { 2 } }\) where \(k\) is a constant
- \(\mathrm { f } ^ { \prime \prime } ( x ) = 0\) at \(P\)
- find the exact value of \(k\),
- find \(\mathrm { f } ( x )\), giving your answer in simplest form.