OCR MEI C3 2008 January — Question 6

Exam BoardOCR MEI
ModuleC3 (Core Mathematics 3)
Year2008
SessionJanuary
TopicImplicit equations and differentiation

6 Fig. 6 shows the curve \(\mathrm { e } ^ { 2 y } = x ^ { 2 } + y\). \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{a66c2da5-46b4-4467-933e-179be04b03b1-3_739_1339_349_404} \captionsetup{labelformat=empty} \caption{Fig. 6}
\end{figure}
  1. Show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 2 x } { 2 \mathrm { e } ^ { 2 y } - 1 }\).
  2. Hence find to 3 significant figures the coordinates of the point P , shown in Fig. 6, where the curve has infinite gradient. Section B (36 marks)