4 Fig. 7 shows the curve \(x ^ { 3 } + y ^ { 3 } = 3 x y\). The point P is a turning point of the curve.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{09d318c7-27b9-43aa-b4a0-e32ea8bd53c5-1_593_531_1573_805}
\captionsetup{labelformat=empty}
\caption{Fig. 7}
\end{figure}
- Show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { y - x ^ { 2 } } { y ^ { 2 } - x }\).
- Hence find the exact \(x\)-coordinate of P .