CAIE FP1 2002 November — Question 6

Exam BoardCAIE
ModuleFP1 (Further Pure Mathematics 1)
Year2002
SessionNovember
TopicImplicit equations and differentiation

6 A curve has equation \(x ^ { 3 } + x y ^ { 2 } - y ^ { 3 } = 3\).
  1. Show that there is no point of the curve at which \(\frac { d y } { d x } = 0\).
  2. Find the values of \(\frac { d y } { d x }\) and \(\frac { d ^ { 2 } y } { d x ^ { 2 } }\) at the point \(( 1 , - 1 )\).