- A curve has equation \(y = \mathrm { f } ( x )\).
The point \(P \left( 4 , \frac { 32 } { 3 } \right)\) lies on the curve.
Given that
- \(\mathrm { f } ^ { \prime \prime } ( x ) = \frac { 4 } { \sqrt { x } } - 3\)
- \(\quad \mathrm { f } ^ { \prime } ( x ) = 5\) at \(P\)
find
- the equation of the tangent to the curve at \(P\), writing your answer in the form \(y = m x + c\), where \(m\) and \(c\) are constants to be found,
- \(\mathrm { f } ( x )\).