Mathematics 9709 · AS & A Level · Differentiation

Differentiation — practice question

The sketch presents the curve with equation $y = \sin 2x + 3\cos 2x$ for $0 \le x \le \pi$. At the points $P$ and $Q$ on the curve, the gradient is $3$.
(i)[2]

Determine an expression for $\frac{dy}{dx}$.

(ii)[8]

After 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 $k_1\cos2x+k_2\sin2x$

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