10. The curve \(C\) has equation
$$y = 12 x ^ { \frac { 5 } { 4 } } - \frac { 5 } { 18 } x ^ { 2 } - 1000 , \quad x > 0$$
- Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\)
- Hence find the coordinates of the stationary point on \(C\).
- Use \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }\) to determine the nature of this stationary point.