CAIE P3 2021 November — Question 9

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2021
SessionNovember
TopicImplicit equations and differentiation

9 The equation of a curve is \(y \mathrm { e } ^ { 2 x } - y ^ { 2 } \mathrm { e } ^ { x } = 2\).
  1. Show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 2 y \mathrm { e } ^ { x } - y ^ { 2 } } { 2 y - \mathrm { e } ^ { x } }\).
  2. Find the exact coordinates of the point on the curve where the tangent is parallel to the \(y\)-axis.