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Intervals where a cubic polynomial increases or decreases

This type of question, asked 5 times: 9 May 2023 S2, 11 May 2023 S1, 15 May 2023 S1, 15 May 2023 S2, 9 May 2024 S2. All 5 questions below, oldest first.

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  1. Question 1

    9 May 2023 S2

    106
    The function f(x)=2x3−6x+5f(x) = 2x^3 - 6x + 5 is an increasing function, if

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  2. Question 2

    11 May 2023 S1

    114
    If f(x)=x3−6x2+9x+3f(x) = x^3 - 6x^2 + 9x + 3 is monotonically decreasing function, then x lies in

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  3. Question 3

    15 May 2023 S1

    118
    If f(x)=x3−10x2+200x−10f(x) = x^{3}-10x^{2}+200x-10, then

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  4. Question 4

    15 May 2023 S2

    118
    The function f(x)=2x3−9x2+12x+2f(x) = 2x^3-9x^2+12x+2 is decreasing in

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  5. Question 5

    9 May 2024 S2

    114
    The range of values of xx for which f(x)=x3+6x2−36x+7f(x) = x^3 + 6x^2 - 36x + 7 is increasing in

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