CAIE P2 2015 June — Question 7

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2015
SessionJune
TopicImplicit equations and differentiation

7 The equation of a curve is $$y ^ { 3 } + 4 x y = 16$$
  1. Show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = - \frac { 4 y } { 3 y ^ { 2 } + 4 x }\).
  2. Show that the curve has no stationary points.
  3. Find the coordinates of the point on the curve where the tangent is parallel to the \(y\)-axis.