Question 7 - A-Level Maths

Given that

\(f ^ { \prime } ( x ) = \frac { 4 x ^ { 2 } + 10 - 7 x ^ { \frac { 1 } { 2 } } } { 4 x ^ { \frac { 1 } { 2 } } }\)
the point \(P ( 4 , - 1 )\) lies on \(C\)
1. (i) find the value of the gradient of \(C\) at \(P\)
  (ii) Hence find the equation of the normal 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.
2. Find \(\mathrm { f } ( x )\).