7 A curve has equation \(y = \frac { x \mathrm { e } ^ { 2 x } } { x + k }\), where \(k\) is a non-zero constant.
- Differentiate \(x \mathrm { e } ^ { 2 x }\), and show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { \mathrm { e } ^ { 2 x } \left( 2 x ^ { 2 } + 2 k x + k \right) } { ( x + k ) ^ { 2 } }\).
- Given that the curve has exactly one stationary point, find the value of \(k\), and determine the exact coordinates of the stationary point.