AQA FP1 2010 June — Question 5

Exam BoardAQA
ModuleFP1 (Further Pure Mathematics 1)
Year2010
SessionJune
TopicDifferentiation from First Principles

5 A curve has equation \(y = x ^ { 3 } - 12 x\).
The point \(A\) on the curve has coordinates ( \(2 , - 16\) ).
The point \(B\) on the curve has \(x\)-coordinate \(2 + h\).
  1. Show that the gradient of the line \(A B\) is \(6 h + h ^ { 2 }\).
  2. Explain how the result of part (a) can be used to show that \(A\) is a stationary point on the curve.
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