Mathematics 9709 · AS & A Level · Differentiation

Differentiation — practice question

The curve is given by $y^3 + 4xy = 16$.
(i)[4]

Show that the derivative satisfies $\frac{dy}{dx} = -\frac{4y}{3y^2 + 4x}$.

(ii)[2]

Show that the curve has no stationary points.

(iii)[4]

Find the coordinates of the point on the curve at which the tangent is parallel to the $y$-axis.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Get $3y^2\frac{dy}{dx}$ by differentiating $y^3$” …

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