AQA C4 2009 January — Question 6

Exam BoardAQA
ModuleC4 (Core Mathematics 4)
Year2009
SessionJanuary
TopicImplicit equations and differentiation

6 A curve is defined by the equation \(x ^ { 2 } y + y ^ { 3 } = 2 x + 1\).
  1. Find the gradient of the curve at the point \(( 2,1 )\).
  2. Show that the \(x\)-coordinate of any stationary point on this curve satisfies the equation $$\frac { 1 } { x ^ { 3 } } = x + 1$$ (4 marks)