6 A curve has the equation
$$y = \frac { 12 + x ^ { 2 } \sqrt { x } } { x } , \quad x > 0$$
- Express \(\frac { 12 + x ^ { 2 } \sqrt { x } } { x }\) in the form \(12 x ^ { p } + x ^ { q }\).
- Hence find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\).
- Find an equation of the normal to the curve at the point on the curve where \(x = 4\).
- The curve has a stationary point \(P\). Show that the \(x\)-coordinate of \(P\) can be written in the form \(2 ^ { k }\), where \(k\) is a rational number.