4. The curve \(C\) has equation \(y = 4 x \sqrt { x } + \frac { 48 } { \sqrt { x } } - \sqrt { 8 } , x > 0\)
- Find, simplifying each term,
- \(\frac { \mathrm { d } y } { \mathrm {~d} x }\)
- \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }\)
- Use part (a) to find the exact coordinates of the stationary point of \(C\).
- Determine whether the stationary point of \(C\) is a maximum or minimum, giving a reason for your answer.