CAIE P1 2012 June — Question 10

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2012
SessionJune
TopicChain Rule

10 It is given that a curve has equation \(y = \mathrm { f } ( x )\), where \(\mathrm { f } ( x ) = x ^ { 3 } - 2 x ^ { 2 } + x\).
  1. Find the set of values of \(x\) for which the gradient of the curve is less than 5 .
  2. Find the values of \(\mathrm { f } ( x )\) at the two stationary points on the curve and determine the nature of each stationary point.