CAIE FP1 2015 November — Question 8

Exam BoardCAIE
ModuleFP1 (Further Pure Mathematics 1)
Year2015
SessionNovember
TopicPolynomial Division & Manipulation

8 The curve \(C\) has equation \(y = \frac { 2 x ^ { 2 } + k x } { x + 1 }\), where \(k\) is a constant. Find the set of values of \(k\) for which \(C\) has no stationary points. For the case \(k = 4\), find the equations of the asymptotes of \(C\) and sketch \(C\), indicating the coordinates of the points where \(C\) intersects the coordinate axes.