CAIE P1 2014 November — Question 9

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2014
SessionNovember
TopicChain Rule

9 The function f is defined for \(x > 0\) and is such that \(\mathrm { f } ^ { \prime } ( x ) = 2 x - \frac { 2 } { x ^ { 2 } }\). The curve \(y = \mathrm { f } ( x )\) passes through the point \(P ( 2,6 )\).
  1. Find the equation of the normal to the curve at \(P\).
  2. Find the equation of the curve.
  3. Find the \(x\)-coordinate of the stationary point and state with a reason whether this point is a maximum or a minimum.