8.
$$f ( x ) \equiv \frac { ( x - 4 ) ^ { 2 } } { 2 x ^ { \frac { 1 } { 2 } } } , x > 0$$
- Find the values of the constants \(A , B\) and \(C\) such that
$$f ( x ) = A x ^ { \frac { 3 } { 2 } } + B x ^ { \frac { 1 } { 2 } } + C x ^ { - \frac { 1 } { 2 } }$$
- Show that
$$f ^ { \prime } ( x ) = \frac { 3 x ^ { 2 } - 8 x - 16 } { 4 x ^ { \frac { 3 } { 2 } } }$$
- Find the coordinates of the stationary point of the curve \(y = \mathrm { f } ( x )\).