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Find the constants of a function from its given extreme points

This type of question, asked 6 times: 3 May 2023 S2, 11 May 2023 S2, 16 May 2023 S1, 16 May 2023 S2, 12 May 2024 S1, 26 Apr 2025 S1. All 6 questions below, oldest first.

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  1. Question 1

    3 May 2023 S2

    118
    If y=alog⁡x+bx2+xy=a\log x+bx^{2}+x has its extreme value at x=−1x=-1 and x=2x=2, then the value of a+ba+b is

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  2. Question 2

    11 May 2023 S2

    112
    If y=alog⁡x+bx2+xy = a\log x+bx^2+x has its extreme values at x=−1x=-1 and x=2x=2, then the value of ab+ba\frac{a}{b}+\frac{b}{a} is

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  3. Question 3

    16 May 2023 S1

    118
    If y=alog⁡x+bx2+xy = a\log x + bx^2 + x has its extremum values at x=−1x = -1 and x=2x = 2, then

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  4. Question 4

    16 May 2023 S2

    150
    If x=−1x=-1 and x=2x=2 are extreme points of f(x)=αlog⁡∣x∣+βx2+xf(x) = \alpha\log|x| + \beta x^2 + x, then

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  5. Question 5

    12 May 2024 S1

    121
    If x=−1x=-1 and x=2x=2 are extreme points of f(x)=αlog⁡∣x∣+βx2+xf(x)=\alpha\log|x|+\beta x^{2}+x, α\alpha and β\beta are constants, then the value of α2+2β\alpha^{2}+2\beta is

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  6. Question 6

    26 Apr 2025 S1

    136
    If y=αlog⁡x+βx3−xy=\alpha \log x+\beta x^{3}-x has extreme values at x=−1x= - 1 and x=1x= 1, then α\alpha and β\beta are respectively

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