2. In this question you must show all stages of your working.
\section*{Solutions relying entirely on calculator technology are not acceptable.}
The curve \(C\) has equation
$$y = 27 x ^ { \frac { 1 } { 2 } } - x ^ { \frac { 3 } { 2 } } - 20 \quad x > 0$$
- Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\), giving each term in simplest form.
- Hence find the coordinates of the stationary point of \(C\).
- Find \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }\) and hence determine the nature of the stationary point of \(C\).