10 At the point \(( 4 , - 1 )\) on a curve, the gradient of the curve is \(- \frac { 3 } { 2 }\). It is given that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = x ^ { - \frac { 1 } { 2 } } + k\), where \(k\) is a constant.
- Show that \(k = - 2\).
- Find the equation of the curve.
- Find the coordinates of the stationary point.
- Determine the nature of the stationary point.