CAIE P1 2009 November — Question 6

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2009
SessionNovember
TopicChain Rule

6 A curve is such that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = k - 2 x\), where \(k\) is a constant.
  1. Given that the tangents to the curve at the points where \(x = 2\) and \(x = 3\) are perpendicular, find the value of \(k\).
  2. Given also that the curve passes through the point \(( 4,9 )\), find the equation of the curve.