OCR MEI Paper 3 2018 June — Question 4

Exam BoardOCR MEI
ModulePaper 3 (Paper 3)
Year2018
SessionJune
TopicCurve Sketching
TypeSketch rational with reciprocal terms

4 In this question you must show detailed reasoning.
A curve has equation \(y = x - 5 + \frac { 1 } { x - 2 }\). The curve is shown in Fig. 4. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{31bc8bde-8d37-4e97-94e2-e3e73aab55e9-5_723_844_424_612} \captionsetup{labelformat=empty} \caption{Fig. 4}
\end{figure}
  1. Determine the coordinates of the stationary points on the curve.
  2. Determine the nature of each stationary point.
  3. Write down the equation of the vertical asymptote.
  4. Deduce the set of values of \(x\) for which the curve is concave upwards.