Edexcel C1 2013 June — Question 9

Exam BoardEdexcel
ModuleC1 (Core Mathematics 1)
Year2013
SessionJune
TopicStandard Integrals and Reverse Chain Rule

9. $$f ^ { \prime } ( x ) = \frac { \left( 3 - x ^ { 2 } \right) ^ { 2 } } { x ^ { 2 } } , \quad x \neq 0$$
  1. Show that \(\mathrm { f } ^ { \prime } ( x ) = 9 x ^ { - 2 } + A + B x ^ { 2 }\),
    where \(A\) and \(B\) are constants to be found.
  2. Find \(\mathrm { f } ^ { \prime \prime } ( x )\). Given that the point \(( - 3,10 )\) lies on the curve with equation \(y = \mathrm { f } ( x )\),
  3. find \(\mathrm { f } ( x )\).