5. The curve \(C\) with equation \(y = \mathrm { f } ( x )\) is such that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = 3 \sqrt { } x + \frac { 12 } { \sqrt { } x } , x > 0\).
- Show that, when \(x = 8\), the exact value of \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) is \(9 \sqrt { } 2\).
The curve \(C\) passes through the point \(( 4,30 )\).
- Using integration, find \(\mathrm { f } ( x )\).