3 The curve \(C\) has equation
$$y = \cosh x - 3 \sinh x$$
- The line \(y = - 1\) meets \(C\) at the point \(( k , - 1 )\).
Show that
$$\mathrm { e } ^ { 2 k } - \mathrm { e } ^ { k } - 2 = 0$$
- Hence find \(k\), giving your answer in the form \(\ln a\).
- Find the \(x\)-coordinate of the point where the curve \(C\) intersects the \(x\)-axis, giving your answer in the form \(p \ln a\).
- Show that \(C\) has no stationary points.
- Show that there is exactly one point on \(C\) for which \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } } = 0\).