CAIE P3 2017 November — Question 5

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2017
SessionNovember
TopicImplicit equations and differentiation

5 The equation of a curve is \(2 x ^ { 4 } + x y ^ { 3 } + y ^ { 4 } = 10\).
  1. Show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = - \frac { 8 x ^ { 3 } + y ^ { 3 } } { 3 x y ^ { 2 } + 4 y ^ { 3 } }\).
  2. Hence show that there are two points on the curve at which the tangent is parallel to the \(x\)-axis and find the coordinates of these points.