OCR MEI C3 — Question 6

Exam BoardOCR MEI
ModuleC3 (Core Mathematics 3)
TopicDifferentiating Transcendental Functions

6 The function \(\mathrm { f } ( x )\) is defined as \(\mathrm { f } ( x ) = \frac { \ln x } { x }\). The graph of the function is shown in Fig. 6 . \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{c7998a08-229a-40d2-ba34-b5f264139295-2_369_675_1930_689} \captionsetup{labelformat=empty} \caption{Fig. 6}
\end{figure}
  1. Give the coordinates of the point, P , where the curve crosses the \(x\)-axis.
  2. Use calculus to find the coordinates of the stationary point, Q , and show that it is a maximum.