CAIE P3 2012 November — Question 7

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2012
SessionNovember
TopicImplicit equations and differentiation

7 The equation of a curve is \(\ln ( x y ) - y ^ { 3 } = 1\).
  1. Show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { y } { x \left( 3 y ^ { 3 } - 1 \right) }\).
  2. Find the coordinates of the point where the tangent to the curve is parallel to the \(y\)-axis, giving each coordinate correct to 3 significant figures.