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Local maximum or minimum points and values of a polynomial

This type of question, asked 3 times: 14 May 2024 S2, 21 Apr 2025 S1, 11 Apr 2026 S1. All 3 questions below, oldest first.

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  1. Question 1

    14 May 2024 S2

    124
    The function f(x)=x3−6x2+9x+2f(x) = x^3 - 6x^2 + 9x + 2 has maximum value when xx is

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  2. Question 2

    21 Apr 2025 S1

    130
    The function x5−5x4+5x3−10x^{5}- 5x^{4}+ 5x^{3}- 10 has a maximum, when xx is equal to

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  3. Question 3

    11 Apr 2026 S1

    74
    The difference between the local extreme values of the function f(x)=2x3−15x2+36x+40f(x) = 2x^3 - 15x^2 + 36x + 40 is ......

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