Edexcel C1 2009 June — Question 9

Exam BoardEdexcel
ModuleC1 (Core Mathematics 1)
Year2009
SessionJune
TopicIndices and Surds

9. $$f ( x ) = \frac { ( 3 - 4 \sqrt { } x ) ^ { 2 } } { \sqrt { } x } , \quad x > 0$$
  1. Show that \(\mathrm { f } ( x ) = 9 x ^ { - \frac { 1 } { 2 } } + A x ^ { \frac { 1 } { 2 } } + B\), where \(A\) and \(B\) are constants to be found.
  2. Find \(\mathrm { f } ^ { \prime } ( x )\).
  3. Evaluate \(\mathrm { f } ^ { \prime } ( 9 )\).