CAIE FP1 2011 November — Question 5

Exam BoardCAIE
ModuleFP1 (Further Pure Mathematics 1)
Year2011
SessionNovember
TopicImplicit equations and differentiation

5 The point \(P ( 2,1 )\) lies on the curve with equation $$x ^ { 3 } - 2 y ^ { 3 } = 3 x y$$ Find
  1. the value of \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) at \(P\),
  2. the value of \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }\) at \(P\).