CAIE P1 2017 November — Question 8

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2017
SessionNovember
TopicChain Rule

8 A curve is such that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = - x ^ { 2 } + 5 x - 4\).
  1. Find the \(x\)-coordinate of each of the stationary points of the curve.
  2. Obtain an expression for \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }\) and hence or otherwise find the nature of each of the stationary points.
  3. Given that the curve passes through the point \(( 6,2 )\), find the equation of the curve.