2026 AHS P1 Q12

Secondary 4

3 marks

Given that \(y=\ln(\cos^5x)\), where \(-\dfrac\pi2<x<\dfrac\pi2\), without finding any coordinates of the stationary points, explain clearly why the curve only has maximum points.[3]

Solution:

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Answer:\(\dfrac{\mathrm{d}^2y}{\mathrm{d}x^2}=-5\sec^2x<0\) throughout the domain, so every stationary point is a maximum.

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