Mathematics 9709 · AS & A Level · Differentiation

Differentiation — practice question

The curve is described by $x^2 - 4xy - 2y^2 = 1$.
(i)[5]

Determine an expression for $\frac{dy}{dx}$ and show that the gradient of the curve at the point $(-1, 2)$ is $-\frac{5}{2}$.

(ii)[3]

Show that the curve has no stationary points.

(iii)[2]

Determine the $x$-coordinate of every point on the curve where 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: Obtain $-4y-4x\dfrac{dy}{dx}$ by applying the product rule

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