5. A curve has equation
$$y = \frac { x ^ { 3 } } { 6 } + 4 \sqrt { x } - 15 \quad x \geqslant 0$$
- Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\), giving the answer in simplest form.
The point \(P \left( 4 , \frac { 11 } { 3 } \right)\) lies on the curve.
- Find the equation of the normal to the curve at \(P\). Write your answer in the form \(a x + b y + c = 0\), where \(a , b\) and \(c\) are integers to be found.
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