Edexcel C1 2008 January — Question 9

Exam BoardEdexcel
ModuleC1 (Core Mathematics 1)
Year2008
SessionJanuary
TopicDifferentiation Applications
TypeFind derivative of polynomial

9. The curve \(C\) has equation \(y = \mathrm { f } ( x ) , x > 0\), and \(\mathrm { f } ^ { \prime } ( x ) = 4 x - 6 \sqrt { } x + \frac { 8 } { x ^ { 2 } }\). Given that the point \(P ( 4,1 )\) lies on \(C\),
  1. find \(\mathrm { f } ( x )\) and simplify your answer.
  2. Find an equation of the normal to \(C\) at the point \(P ( 4,1 )\).