(a)[3]
Show that the gradient of the curve at the point with parameter $\theta$ is $-2\sin\theta\cos^3\theta$.
(b)[4]
The gradient of the curve reaches its maximum value at the point $P$. Find the exact value of the $x$-coordinate of $P$.
Mathematics 9709 · AS & A Level · Differentiation
Differentiation — practice question
The sketch shows the curve defined by the parametric equations $x = \tan\theta$, $y = \cos^2\theta$, for $-\frac{1}{2}\pi < \theta < \frac{1}{2}\pi$.
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “State either $\dfrac{dx}{d\theta}=\sec^2\theta$ or $\dfrac{dy}{d\theta}=-2\sin\theta\cos\theta$” …
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