CAIE FP1 2017 November — Question 5

Exam BoardCAIE
ModuleFP1 (Further Pure Mathematics 1)
Year2017
SessionNovember
TopicImplicit equations and differentiation

5 The curve \(C\) has equation \(2 x ^ { 3 } + 3 x ^ { 2 } y - 3 y ^ { 3 } - 16 = 0\).
  1. Find the coordinates of the point \(A\) on \(C\) at which \(\frac { \mathrm { d } y } { \mathrm {~d} x } = 0\) and \(x \neq 0\).
  2. Find the value of \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }\) at \(A\).