CAIE P2 2005 November — Question 6

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2005
SessionNovember
TopicStandard Integrals and Reverse Chain Rule

6 A curve is such that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \mathrm { e } ^ { 2 x } - 2 \mathrm { e } ^ { - x }\). The point \(( 0,1 )\) lies on the curve.
  1. Find the equation of the curve.
  2. The curve has one stationary point. Find the \(x\)-coordinate of this point and determine whether it is a maximum or a minimum point.