- In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.
The curve \(C\) has equation \(y = \mathrm { f } ( x ) , x > 0\)
Given that
- \(\mathrm { f } ^ { \prime } ( \mathrm { x } ) = \frac { 12 } { \sqrt { \mathrm { x } } } + \frac { x } { 3 } - 4\)
- the point \(P ( 9,8 )\) lies on \(C\)
- find, in simplest form, \(\mathrm { f } ( x )\)
The line \(l\) is the normal to \(C\) at \(P\)
Find the coordinates of the point at which \(l\) crosses the \(y\)-axis.