CAIE P1 2020 March — Question 10

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2020
SessionMarch
TopicChain Rule

10 The gradient of a curve at the point \(( x , y )\) is given by \(\frac { \mathrm { d } y } { \mathrm {~d} x } = 2 ( x + 3 ) ^ { \frac { 1 } { 2 } } - x\). The curve has a stationary point at \(( a , 14 )\), where \(a\) is a positive constant.
  1. Find the value of \(a\).
  2. Determine the nature of the stationary point.
  3. Find the equation of the curve.