The curve \(C\) has equation \(y = \frac { 1 } { 8 } x ^ { 3 } - \frac { 24 } { \sqrt { x } } + 1\)
Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\), giving the answer in its simplest form.
(3)
The point \(P ( 4 , - 3 )\) lies on \(C\).
Find the equation of the tangent to \(C\) at the point \(P\). Write your answer in the form \(y = m x + c\), where \(m\) and \(c\) are constants to be found.