6. A curve has the equation \(y = \mathrm { e } ^ { 3 x } \cos 2 x\).
- Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\).
- Show that \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } } = \mathrm { e } ^ { 3 x } ( 5 \cos 2 x - 12 \sin 2 x )\).
The curve has a stationary point in the interval \([ 0,1 ]\).
- Find the \(x\)-coordinate of the stationary point to 3 significant figures.
- Determine whether the stationary point is a maximum or minimum point and justify your answer.