AQA FP1 2015 June — Question 8

Exam BoardAQA
ModuleFP1 (Further Pure Mathematics 1)
Year2015
SessionJune
TopicCurve Sketching
TypeRange restriction problems

8 A curve \(C\) has equation $$y = \frac { x ( x - 3 ) } { x ^ { 2 } + 3 }$$
  1. State the equation of the asymptote of \(C\).
  2. The line \(y = k\) intersects the curve \(C\). Show that \(4 k ^ { 2 } - 4 k - 3 \leqslant 0\).
  3. Hence find the coordinates of the stationary points of the curve \(C\). (No credit will be given for solutions based on differentiation.)
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