6. The curve \(C\) has equation \(y = \mathrm { f } ( x )\) where \(x > 0\)
Given that
- \(\mathrm { f } ^ { \prime } ( x ) = \frac { ( x + 3 ) ^ { 2 } } { x \sqrt { x } }\)
- the point \(P ( 4,20 )\) lies on \(C\)
- (i) find the value of the gradient at \(P\)
(ii) Hence find the equation of the tangent to \(C\) at \(P\), giving your answer in the form \(a x + b y + c = 0\) where \(a , b\) and \(c\) are integers to be found. - Find \(\mathrm { f } ( x )\), simplifying your answer.