A value of c for which the conclusion of Mean Value Theorem holds for the function f(x) = _e x on the interval [1, 3] is: - Mathematics MCQ AIEEE 2007 2026 | ExamTest.live

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A value of c for which the conclusion of Mean Value Theorem holds for the function f (x) = lo g_{e} x on the interval [1, 3] is:

Solution & Step-by-step Explanation

According to the Lagrange Mean Value Theorem, there exists c \in (1, 3) such that: f^{'} (c) = \frac{f ( 3 ) - f ( 1 )}{3 - 1} Given f (x) = lo g_{e} x ⟹ f^{'} (x) = 1/ x . \frac{1}{c} = \frac{lo g _{e} 3 - lo g _{e} 1}{2} \frac{1}{c} = \frac{lo g _{e} 3}{2} c = \frac{2}{lo g _{e} 3} = 2 lo g_{3} e

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A value of c for which the conclusion of Mean Value Theorem holds for the function f (x) = lo g_{e} x on the interval [1, 3] is:

2 lo g_{3} e

\frac{1}{2 l o g _{e} 3}

lo g_{3} e

lo g_{e} 3

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