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}
- Determine the coordinates of the stationary points on the curve.
- Determine the nature of each stationary point.
- Write down the equation of the vertical asymptote.
- Deduce the set of values of \(x\) for which the curve is concave upwards.