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Find the constants in a function given that Rolle's theorem holds

This type of question, asked 9 times: 2 May 2023 S1, 13 May 2024 S2, 25 Apr 2025 S1, 25 Apr 2025 S2, 11 Apr 2026 S2, 15 Apr 2026 S1, 18 Apr 2026 S2, 12 May 2026 S2, 14 May 2026 S2. All 9 questions below, oldest first.

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  1. Question 1

    2 May 2023 S1

    138
    If Rolle's theorem holds for the function f(x)=x3+bx2+ax+5f(x) = x^3 + bx^2 + ax + 5 on [1,3][1,3] with c=2+13c = 2 + \dfrac{1}{\sqrt{3}}, then the values of aa and bb respectively are

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  2. Question 2

    13 May 2024 S2

    108
    If Rolle's theorem holds for the function f(x)=x3+bx2+ax+5f(x)=x^3+bx^2+ax+5 on [1,3][1,3] with c=2+13c=2+\frac{1}{\sqrt{3}}, then the values of aa and bb respectively are

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  3. Question 3

    25 Apr 2025 S1

    110
    If Rolle's theorem holds for the function x3+ax2+bx,1≤x≤2x^{3}+ax^{2}+bx,1 \leq x\leq 2 at the point 43\frac{4}{3}, then the values of aa and bb are respectively

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  4. Question 4

    25 Apr 2025 S2

    142
    The function f(x)=x3−6x2+ax+bf(x) =x^{3}- 6x^{2}+ax+b satisfies the conditions of Rolle's theorem in [1,3]. Then the values of aa and bb are respectively

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  5. Question 5

    11 Apr 2026 S2

    74
    If the function f(x)=ax3+bx2+11x−6f(x) = ax^3 + bx^2 + 11x - 6, defined on [1,3][1, 3], satisfies all the conditions of Rolle's theorem for c=2+13c = 2 + \dfrac{1}{\sqrt{3}}, then

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  6. Question 6

    15 Apr 2026 S1

    74
    If the function f(x)=ax3−bx2−8x−4f(x) = ax^3 - bx^2 - 8x - 4 satisfies Roll's theorem in [1,3][1, 3], if f′(2)=0f'(2) = 0 then a−ba - b is equal to...

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  7. Question 7

    18 Apr 2026 S2

    76
    If the function f(x)=ax2+bx+sin⁡xf(x) = ax^2 + bx + \sin x satisfies all the conditions of Rolle's theorem on [0,π][0, \pi] and the slope of the tangent to the curve y=f(x)y = f(x) at x=π4x = \dfrac{\pi}{4} is zero, then a−b=a - b =

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  8. Question 8

    12 May 2026 S2

    74
    If Rolle's theorem holds for the function f(x)=x3+px2+qx+5,x∈[1,3]f(x) = x^3 + px^2 + qx + 5, x \in [1, 3] with c=2+13c = 2 + \dfrac{1}{\sqrt{3}}, then the values of pp and qq are respectively...

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  9. Question 9

    14 May 2026 S2

    78
    If Rolle's theorem holds for the function f(x)=x2−px+10f(x) = x^2 - px + 10, x∈[0,4]x \in [0, 4] with c=2c = 2, then p=p =

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