Sketch on the axes below the graphs of \(y = \sinh x\) and \(y = \cosh x\).
Use your graphs to explain why the equation
$$( k + \sinh x ) \cosh x = 0$$
where \(k\) is a constant, has exactly one solution.
A curve \(C\) has equation \(y = 6 \sinh x + \cosh ^ { 2 } x\). Show that \(C\) has only one stationary point and show that its \(y\)-coordinate is an integer.
\includegraphics[max width=\textwidth, alt={}, center]{53d742f4-923b-478c-8ae6-ada6c0bb4a7e-2_560_704_1416_171}
\includegraphics[max width=\textwidth, alt={}, center]{53d742f4-923b-478c-8ae6-ada6c0bb4a7e-2_560_711_1416_964}