10 A curve is defined for \(x > 0\) and is such that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = x + \frac { 4 } { x ^ { 2 } }\). The point \(P ( 4,8 )\) lies on the curve.
- Find the equation of the curve.
- Show that the gradient of the curve has a minimum value when \(x = 2\) and state this minimum value.