10 The equation of a curve is \(y = 2 x + \frac { 8 } { x ^ { 2 } }\).
- Obtain expressions for \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) and \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }\).
- Find the coordinates of the stationary point on the curve and determine the nature of the stationary point.
- Show that the normal to the curve at the point \(( - 2 , - 2 )\) intersects the \(x\)-axis at the point \(( - 10,0 )\).
- Find the area of the region enclosed by the curve, the \(x\)-axis and the lines \(x = 1\) and \(x = 2\).