6 A curve has equation \(y = \frac { 9 \mathrm { e } ^ { 2 x } + 16 } { \mathrm { e } ^ { x } - 1 }\).
- Show that the \(x\)-coordinate of any stationary point on the curve satisfies the equation
$$\mathrm { e } ^ { x } \left( 3 \mathrm { e } ^ { x } - 8 \right) \left( 3 \mathrm { e } ^ { x } + 2 \right) = 0$$
- Hence show that the curve has only one stationary point and find its exact coordinates.