(i)[4]
Show that, after simplification, $\frac{dy}{dx} = -12\cos t$.
(ii)[2]
Determine the coordinates of $M$.
(iii)[4]
Determine the gradient of the curve at $P$ and at $Q$.
Mathematics 9709 · AS & A Level · Differentiation
Differentiation — practice question
The diagram displays the curve defined by the parametric equations $x = 2 - \cos t$, $y = 1 + 3\cos 2t$, for $0 < t < \pi$. The minimum point is $M$, and the curve intersects the $x$-axis at $P$ and $Q$.
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This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “State the derivatives $\frac{dx}{dt}=\sin t$ and $\frac{dy}{dt}=-6\sin2t$.” …
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