7. The curve \(C\) has equation \(y = \mathrm { f } ( x ) , x > 0\)
Given that
- \(\mathrm { f } ^ { \prime } ( x ) = \frac { 2 } { \sqrt { x } } + \frac { A } { x ^ { 2 } } + 3\), where \(A\) is a constant
- \(\mathrm { f } ^ { \prime \prime } ( x ) = 0\) when \(x = 4\)
- find the value of \(A\).
Given also that
- \(\mathrm { f } ( x ) = 8 \sqrt { 3 }\), when \(x = 12\)
- find \(\mathrm { f } ( x )\), giving each term in simplest form.