10 The curve, \(C\), has equation \(y = \frac { x } { \cosh x }\)
10
- Show that the \(x\)-coordinates of any stationary points of \(C\) satisfy the equation \(\tanh x = \frac { 1 } { x }\)
[0pt]
[3 marks]
10 - Sketch the graphs of \(y = \tanh x\) and \(y = \frac { 1 } { x }\) on the axes below.
[0pt]
[2 marks]
\includegraphics[max width=\textwidth, alt={}, center]{a155b39a-6835-4d62-a481-41ef822bbd5f-14_1151_1226_1461_358}
10
- (ii) Hence determine the number of stationary points of the curve \(C\).
10
- Show that \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } } + y = 0\) at each of the stationary points of the curve \(C\).
[0pt]
[4 marks]