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A value of c for which conclusion of Mean Value Theorem holds for the function f (x) = loge x on the interval [1, 3] is
  • a)
    log3e
  • b)
    loge3
  • c)
    2 log3e
  • d)
Correct answer is option 'C'. Can you explain this answer?
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A value of c for which conclusion of Mean Value Theorem holds for the ...
Using Lagrange's Mean Value Theorem
Let f (x) be a function defined on [a, b]

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A value of c for which conclusion of Mean Value Theorem holds for the ...
Using Lagrange's Mean Value Theorem
Let f (x) be a function defined on [a, b]

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Community Answer
A value of c for which conclusion of Mean Value Theorem holds for the ...
We know,

f'(X)={f(b) - f(a)}/(b - a)

1/X = {f(3) - f(1)}/(3-1)

1/C = (ln3 - 0)/2

1/C = ln3/2

C = 2/ln3

C = 2ln e note:- {log a = 1/log b}
3 b a
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A value of c for which conclusion of Mean Value Theorem holds for the function f (x) = loge x on the interval [1, 3] isa)log3eb)loge3c)2 log3ed)Correct answer is option 'C'. Can you explain this answer?
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