Edexcel FP3 2013 June — Question 4

Exam BoardEdexcel
ModuleFP3 (Further Pure Mathematics 3)
Year2013
SessionJune
TopicHyperbolic functions

4. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{bd4cd798-61ae-49b6-a297-bb4b9ed15fb1-05_384_1040_226_438} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} Figure 1 shows part of the curve with equation $$y = 40 \operatorname { arcosh } x - 9 x , \quad x \geqslant 1$$ Use calculus to find the exact coordinates of the turning point of the curve, giving your answer in the form \(\left( \frac { p } { q } , r \ln 3 + s \right)\), where \(p , q , r\) and \(s\) are integers.