Question: Consider the curve given by \({{x}^{2}}+4{{y}^{2}}=7+3xy\)

1. Show that \(\frac{dy}{dx}=\frac{3y-2x}{8y-3x}\)
2. Show that there is a point P with x -coordinate 3 at which the line tangent to the curve P is horizontal. Find the y -coordinate of P .
3. Find the value of \(\frac{{{d}^{2}}y}{d{{x}^{2}}}\) at the point P from part b .

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