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A value of C for which the conclusion...

A value of C for which the conclusion of Mean Value Theorem holds for the function `f(x)""=""(log)_e x` on the interval [1, 3] is (1) `2(log)_3e` (2) `1/2""(log)_e3` (3) `(log)_3e` (4) `(log)_e3`

A

`2 log_(3) e`

B

`(1)/(2) log_(e) 3`

C

`log_(3)e`

D

`log_(e) 3`

Text Solution

AI Generated Solution

To solve the problem, we will use the Mean Value Theorem (MVT). The theorem states that if a function is continuous on a closed interval [a, b] and differentiable on the open interval (a, b), then there exists at least one point c in (a, b) such that: \[ f'(c) = \frac{f(b) - f(a)}{b - a} \] ### Step-by-Step Solution: 1. **Identify the function and interval**: - The function given is \( f(x) = \log_e x \). ...
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