(i)[4]
Show that $\frac{dy}{dx} = 6\cos^4 \theta - 3\cos^2 \theta$ for this curve.
(ii)[3]
Find the coordinates of the stationary point on the curve.
(iii)[2]
Find the gradient of the curve at the point $(2\sqrt{3}, \tfrac{3}{2}\sqrt{3})$.
Mathematics 9709 · AS & A Level · Differentiation
Differentiation — practice question
The curve is given by the parametric equations $x = 2\tan \theta$, $y = 3\sin 2\theta$, where $0 \leq \theta \leq \frac{1}{2}\pi$.
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This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Obtain $\dfrac{dx}{d\theta}=2\sec^2\theta$ and $\dfrac{dy}{d\theta}=6\cos2\theta$.” …
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