9231 P11 - Jun 2013 - Q10 - 13 marks
6395
The curve \(C\) has equation \(y=\frac{2 x^{2}-3 x-2}{x^{2}-2 x+1}\). State the equations of the asymptotes of \(C\).
Show that \(y \leqslant \frac{25}{12}\) at all points of \(C\).
Find the coordinates of any stationary points of \(C\).
Sketch \(C\), stating the coordinates of any intersections of \(C\) with the coordinate axes and the asymptotes.
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