(i)[4]
Show that the result is $\frac{dy}{dx} = \frac{3x^2y - 3y^3}{9xy^2 - x^3}$.
(ii)[4]
Hence show that the curve has only two points where the tangent is parallel to the $x$-axis, and determine the coordinates of those points.
Mathematics 9709 · AS & A Level · Differentiation
Differentiation — practice question
The curve is defined by $x^3y - 3xy^3 = 2a^4$, with $a$ as a non-zero constant.
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This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Give or indicate $3x^2y+x^3\frac{dy}{dx}$ as the derivative of $x^3y$” …
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