9231 P11 - Nov 2011 - Q5 - 7 marks
6548
The point \(P(2,1)\) lies on the curve with equation
\(x^{3}-2 y^{3}=3 x y .\)
Find
(i) the value of \(\frac{\mathrm{d} y}{\mathrm{~d} x}\) at \(P\),
(ii) the value of \(\frac{\mathrm{d}^{2} y}{\mathrm{~d} x^{2}}\) at \(P\).
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