AQA FP1 2005 June — Question 4

Exam BoardAQA
ModuleFP1 (Further Pure Mathematics 1)
Year2005
SessionJune
TopicDifferentiation from First Principles

4 The function f is defined for all real values of \(x\) by $$\mathrm { f } ( x ) = x ^ { 3 } + x$$
  1. Express \(\mathrm { f } ( 2 + h ) - \mathrm { f } ( 2 )\) in the form $$p h + q h ^ { 2 } + r h ^ { 3 }$$ where \(p , q\) and \(r\) are integers.
  2. Use your answer to part (a) to find the value of \(\mathrm { f } ^ { \prime } ( 2 )\).