3. A curve \(C\) has equation
$$y = x ^ { 2 } \mathrm { e } ^ { x }$$
- Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\), using the product rule for differentiation.
- Hence find the coordinates of the turning points of \(C\).
- Find \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }\).
- Determine the nature of each turning point of the curve \(C\).