CAIE P1 2023 June — Question 11

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2023
SessionJune
TopicChain Rule

11 The equation of a curve is such that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = 6 x ^ { 2 } - 30 x + 6 a\), where \(a\) is a positive constant. The curve has a stationary point at \(( a , - 15 )\).
  1. Find the value of \(a\).
  2. Determine the nature of this stationary point.
  3. Find the equation of the curve.
  4. Find the coordinates of any other stationary points on the curve.