CAIE P1 2021 November — Question 9

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2021
SessionNovember
TopicStandard Integrals and Reverse Chain Rule

9 A curve has equation \(y = \mathrm { f } ( x )\), and it is given that \(\mathrm { f } ^ { \prime } ( x ) = 2 x ^ { 2 } - 7 - \frac { 4 } { x ^ { 2 } }\).
  1. Given that \(\mathrm { f } ( 1 ) = - \frac { 1 } { 3 }\), find \(\mathrm { f } ( x )\).
  2. Find the coordinates of the stationary points on the curve.
  3. Find \(\mathrm { f } ^ { \prime \prime } ( x )\).
  4. Hence, or otherwise, determine the nature of each of the stationary points.