CAIE P1 2015 November — Question 9

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2015
SessionNovember
TopicDifferential equations

9 The curve \(y = \mathrm { f } ( x )\) has a stationary point at \(( 2,10 )\) and it is given that \(\mathrm { f } ^ { \prime \prime } ( x ) = \frac { 12 } { x ^ { 3 } }\).
  1. Find \(\mathrm { f } ( x )\).
  2. Find the coordinates of the other stationary point.
  3. Find the nature of each of the stationary points.