Mathematics 9709 · AS & A Level · Differentiation

Differentiation — practice question

The diagram represents the curve given by $y = \sin 2x + 3\cos 2x$ for $0 \leq x \leq \pi$. At points $P$ and $Q$ on the curve, the gradient is $3$.
(i)[2]

Find a formula for $\frac{dy}{dx}$.

(ii)[8]

By first writing $\frac{dy}{dx}$ as $R\cos(2x + \alpha)$, where $R > 0$ and $0 < \alpha < \tfrac{1}{2}\pi$, determine the $x$-coordinates of $P$ and $Q$, giving answers correct to $4$ significant figures.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “State an expression in the form $k_1\cos 2x+k_2\sin 2x$” …

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