CAIE P2 2020 November — Question 5

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2020
SessionNovember
TopicImplicit equations and differentiation

5 The equation of a curve is \(2 \mathrm { e } ^ { 2 x } y - y ^ { 3 } + 4 = 0\).
  1. Show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 4 \mathrm { e } ^ { 2 x } y } { 3 y ^ { 2 } - 2 \mathrm { e } ^ { 2 x } }\).
  2. The curve passes through the point \(( 0,2 )\). Find the equation of the tangent to the curve at this point, giving your answer in the form \(a x + b y + c = 0\).
  3. Show that the curve has no stationary points.