Edexcel C1 2007 January — Question 7

Exam BoardEdexcel
ModuleC1 (Core Mathematics 1)
Year2007
SessionJanuary
TopicIndefinite & Definite Integrals

7. The curve \(C\) has equation \(y = \mathrm { f } ( x ) , x \neq 0\), and the point \(P ( 2,1 )\) lies on \(C\). Given that $$f ^ { \prime } ( x ) = 3 x ^ { 2 } - 6 - \frac { 8 } { x ^ { 2 } } ,$$
  1. find \(\mathrm { f } ( x )\).
  2. Find an equation for the tangent to \(C\) at the point \(P\), giving your answer in the form \(y = m x + c\), where \(m\) and \(c\) are integers.