OCR FP2 2010 January — Question 8

Exam BoardOCR
ModuleFP2 (Further Pure Mathematics 2)
Year2010
SessionJanuary
TopicIntegration with Partial Fractions

8 The equation of a curve is $$y = \frac { k x } { ( x - 1 ) ^ { 2 } } ,$$ where \(k\) is a positive constant.
  1. Write down the equations of the asymptotes of the curve.
  2. Show that \(y \geqslant - \frac { 1 } { 4 } k\).
  3. Show that the \(x\)-coordinate of the stationary point of the curve is independent of \(k\), and sketch the curve.