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Greatest or least value of a cubic on a set given by a quadratic inequality

This type of question, asked 5 times: 2 May 2023 S2, 3 May 2023 S2, 11 May 2023 S2, 9 May 2024 S2, 14 May 2024 S1. All 5 questions below, oldest first.

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  1. Question 1

    2 May 2023 S2

    129
    The maximum value of the function f(x)=3x3−18x2+27x−40f(x) = 3x^3 - 18x^2 + 27x - 40 on the set S={x∈R:x2+30≤11x}S = \{x\in\mathbb{R} : x^2+30 \leq 11x\} is

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  2. Question 2

    3 May 2023 S2

    137
    The minimum value of the function f(x)=2x3−15x2+36x−48f(x)=2x^{3}-15x^{2}+36x-48 on the set A={x∣x2+20≤9x}A=\{x\mid x^{2}+20\leq9x\} is

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  3. Question 3

    11 May 2023 S2

    133
    The maximum value of the function f(x)=2x3−15x2+36x−48f(x) = 2x^3-15x^2+36x-48 on the set A={x∣x2+20≤9x}A = \{x\mid x^2+20\leq9x\} is

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  4. Question 4

    9 May 2024 S2

    115
    The maximum value of the function f(x)=3x3−18x2+27x−40f(x) = 3x^3 - 18x^2 + 27x - 40 on the set S={x∈R:x2+30≤11x}S = \{x \in \mathbb{R} : x^2 + 30 \leq 11x\} is

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  5. Question 5

    14 May 2024 S1

    111
    The maximum value of the function f(x)=3x3−18x2+27x−40f(x)=3x^3-18x^2+27x-40 on the set S={x∈R ∣ x2+30≤11x}S=\{x\in\mathbb{R}\,|\,x^2+30\leq11x\} is

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