CAIE P1 2024 November — Question 3

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2024
SessionNovember
TopicDifferentiation from First Principles

3 The equation of a curve is \(y = 2 x ^ { 2 } - 3\). Two points \(A\) and \(B\) with \(x\)-coordinates 2 and \(( 2 + h )\) respectively lie on the curve.
  1. Find and simplify an expression for the gradient of the chord \(A B\) in terms of \(h\).
  2. Explain how the gradient of the curve at the point \(A\) can be deduced from the answer to part (a), and state the value of this gradient.