CAIE P2 2016 March — Question 7

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2016
SessionMarch
TopicImplicit equations and differentiation

7 The equation of a curve is \(2 x ^ { 3 } + y ^ { 3 } = 24\).
  1. Express \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) in terms of \(x\) and \(y\), and show that the gradient of the curve is never positive.
  2. Find the coordinates of the two points on the curve at which the gradient is - 2 .