CAIE P3 2023 November — Question 7 5 marks

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2023
SessionNovember
Marks5
TopicImplicit equations and differentiation

7 The equation of a curve is \(x ^ { 3 } + y ^ { 2 } + 3 x ^ { 2 } + 3 y = 4\).
  1. Show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = - \frac { 3 x ^ { 2 } + 6 x } { 2 y + 3 }\).
  2. Hence find the coordinates of the points on the curve at which the tangent is parallel to the \(x\)-axis. [5]