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2025 YIJC Promo Q6
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2025 YIJC Promo Q6
Junior College 1
6 marks
Differentiate \(\sqrt{x}\cos 3x\) with respect to \(x\).
[2]
The curve \(C\) has equation \(2xy-y^3=5\).
Express \(\dfrac{dy}{dx}\) in terms of \(x\) and \(y\).
[2]
Without using a calculator, show that \(C\) does not have any stationary points.
[2]
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Answer:
\(\dfrac{d}{dx}(\sqrt{x}\cos3x)=\dfrac{\cos3x}{2\sqrt{x}}-3\sqrt{x}\sin3x\); the curve has no stationary points
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