8 A curve has equation \(y = ( x + 2 ) \mathrm { e } ^ { - x }\).
- Find the coordinates of the points where the curve cuts the axes.
- Find the coordinates of the stationary point, S , on the curve.
- By evaluating \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }\) at S , determine whether the stationary point is a maximum or a minimum.
- Sketch the curve in the domain \(- 3 < x < 3\).
- Find where the normal to the curve at the point \(( 0,2 )\) cuts the curve again.
- Find the area of the region bounded by the curve, the \(x\)-axis and the lines \(x = 1\) and \(x = 3\).