CAIE FP1 2004 November — Question 7

Exam BoardCAIE
ModuleFP1 (Further Pure Mathematics 1)
Year2004
SessionNovember
TopicImplicit equations and differentiation

7 The curve \(C\) has equation $$x y + ( x + y ) ^ { 5 } = 1$$
  1. Show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = - \frac { 5 } { 6 }\) at the point \(A ( 1,0 )\) on \(C\).
  2. Find the value of \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }\) at \(A\).