AQA C2 2007 June — Question 5

Exam BoardAQA
ModuleC2 (Core Mathematics 2)
Year2007
SessionJune
TopicChain Rule

5 A curve is defined for \(x > 0\) by the equation $$y = \left( 1 + \frac { 2 } { x } \right) ^ { 2 }$$ The point \(P\) lies on the curve where \(x = 2\).
  1. Find the \(y\)-coordinate of \(P\).
  2. Expand \(\left( 1 + \frac { 2 } { x } \right) ^ { 2 }\).
  3. Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\).
  4. Hence show that the gradient of the curve at \(P\) is - 2 .
  5. Find the equation of the normal to the curve at \(P\), giving your answer in the form \(x + b y + c = 0\), where \(b\) and \(c\) are integers.