CAIE P2 2020 November — Question 8

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2020
SessionNovember
TopicProduct & Quotient Rules

8 A curve has equation \(y = f ( x )\) where \(f ( x ) = \frac { 4 x ^ { 3 } + 8 x - 4 } { 2 x - 1 }\).
  1. Find an expression for \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) and hence find the coordinates of each of the stationary points of the curve \(y = \mathrm { f } ( x )\).
  2. Divide \(4 x ^ { 3 } + 8 x - 4\) by ( \(2 x - 1\) ), and hence find \(\int \mathrm { f } ( x ) \mathrm { d } x\).
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