- The curve \(C\) has equation
$$y = \frac { x ^ { 2 } } { 3 } + \frac { 4 } { \sqrt { x } } + \frac { 8 } { 3 x } - 5 \quad x > 0$$
- Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\), giving your answer in simplest form.
The point \(P ( 4,3 )\) lies on \(C\).
- Find the equation of the normal to \(C\) at the point \(P\). Write your answer in the form \(a x + b y + c = 0\), where \(a , b\) and \(c\) are integers to be found.