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Condition on a constant for a function to be increasing or decreasing for all real x

This type of question, asked 3 times: 16 May 2023 S2, 21 Apr 2025 S2, 11 Apr 2026 S2. All 3 questions below, oldest first.

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  1. Question 1

    16 May 2023 S2

    120
    If f(x)=asin⁡x+bcos⁡xcsin⁡x+dcos⁡xf(x) = \frac{a\sin x + b\cos x}{c\sin x + d\cos x} is decreasing for all xx, then

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  2. Question 2

    21 Apr 2025 S2

    116
    If f(x)=ksinx+2cos⁡xsin⁡x+cos⁡xf(x) =\frac{ksinx+ 2\cos x}{\sin x+ \cos x} is strictly increasing for all real values of xx, then

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  3. Question 3

    11 Apr 2026 S2

    76
    The value of kk such that the function f(x)=sin⁡x−cos⁡x−kx+bf(x) = \sin x - \cos x - kx + b is strictly decreasing for all real xx is

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