CAIE P1 2002 November — Question 8

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2002
SessionNovember
TopicChain Rule

8 A curve has equation \(y = x ^ { 3 } + 3 x ^ { 2 } - 9 x + k\), where \(k\) is a constant.
  1. Write down an expression for \(\frac { \mathrm { d } y } { \mathrm {~d} x }\).
  2. Find the \(x\)-coordinates of the two stationary points on the curve.
  3. Hence find the two values of \(k\) for which the curve has a stationary point on the \(x\)-axis.