7. Fig. 10 shows the graph of \(x ^ { 3 } + y ^ { 3 } = x y\).
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{14f14bf3-88ee-413c-a62d-0914f41a485d-16_538_527_251_785}
\captionsetup{labelformat=empty}
\caption{Fig. 10}
\end{figure}
- Find an expression for \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) in terms of \(x\) and \(y\).
- P is the maximum point on the curve. The parabola \(y = k x ^ { 2 }\) intersects the curve at P . Find the value of the constant \(k\).
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