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Value of c in Lagrange's mean value theorem for a given function on an interval

This type of question, asked 9 times: 2 May 2023 S2, 9 May 2023 S1, 10 May 2023 S2, 9 May 2024 S1, 10 May 2024 S2, 13 May 2024 S2, 19 Apr 2025 S1, 21 Apr 2025 S2, 14 May 2026 S1. All 9 questions below, oldest first.

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  1. Question 1

    2 May 2023 S2

    117
    The value of C for which the Mean Value Theorem holds for f(x)=log⁡exf(x) = \log_e x on [1,3][1,3] is

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  2. Question 2

    9 May 2023 S1

    135
    If Mean Value Theorem holds for the function f(x)=(x−1)(x−2)(x−3)f(x)=(x-1)(x-2)(x-3), x∈[0,4]x\in[0,4] then the values of c as per the theorem are

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  3. Question 3

    10 May 2023 S2

    109
    Let f(x)=(x−1)(x−2)(x−3),x∈[0,4]f(x) = (x-1)(x-2)(x-3), x\in[0,4]. Values of C if LMVT can be applied.

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  4. Question 4

    9 May 2024 S1

    126
    The value of cc of Lagrange's mean value theorem for f(x)=25−x2f(x)=\sqrt{25-x^2} on [1,5][1,5] is

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  5. Question 5

    10 May 2024 S2

    131
    The value of cc for the function f(x)=log⁡xf(x)=\log x on [1,e][1,e] if LMVT can be applied, is

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  6. Question 6

    13 May 2024 S2

    123
    A(1,-3), B(4,3) are two points on the curve y=x−4xy=x-\frac{4}{x}. The points on the curve, the tangents at which are parallel to the chord AB, are

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  7. Question 7

    19 Apr 2025 S1

    141
    In the mean value theorem, f′(c)=f(b)−f(a)b−af^{'}(c) =\frac{f(b) -f(a)}{b-a}, if a=0, b=12a = 0,\text{ }b =\frac{1}{2} and f(x)=x(x−1)(x−2)f(x) =x(x- 1)(x- 2), then the value of cc is

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  8. Question 8

    21 Apr 2025 S2

    141
    The abscissae of the points of the curve y=x3y=x^{3} are in the interval [−2,2]\lbrack - 2,2\rbrack, where the slope of the tangents can be obtained by mean value theorem for the interval [−2,2]\lbrack - 2,2\rbrack are

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  9. Question 9

    14 May 2026 S1

    77
    In the Lagrange's Mean Value Theorem, f(b)−f(a)=(b−a)f′(c);(a<c<b)f(b) - f(a) = (b - a)f'(c); (a < c < b). If a=2,b=4a = 2, b = 4 and f(x)=x2−4f(x) = \sqrt{x^2 - 4}, then the value of cc is

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