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Value of c for which conclusion of Mean Value Theorem holds for the function f(x) = logₑ x on the interval [1, 3] is
- log₃ e
- logₑ 3
- 2 log₃ e
- 1/2 log₃ e
Correct answer: 2 log₃ e
Solution
For f(x)=ln x on [1,3], f'(c) = (f(3)-f(1))/(3-1) = (ln3)/2. Since f'(c)=1/c, c = 2/ln3 = 2 log_3 e.
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