CAIE Further Paper 2 2020 November — Question 5

Exam BoardCAIE
ModuleFurther Paper 2 (Further Paper 2)
Year2020
SessionNovember
TopicImplicit equations and differentiation

5 The curve \(C\) has equation $$y ^ { 2 } + ( x y + 1 ) ^ { 2 } = 5$$
  1. Show that, at the point \(( 1,1 )\) on \(C , \frac { \mathrm { dy } } { \mathrm { dx } } = - \frac { 2 } { 3 }\).
  2. Find the value of \(\frac { d ^ { 2 } y } { d x ^ { 2 } }\) at the point \(( 1,1 )\).