The value of $c$ for which the conclusio

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Continuity and Differentiability

Question:

The 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

Options:

$2 \log _3 e$

$\frac{1}{2} \log _e 3$

$\log _3 e$

$\log _e 3$

Correct Answer:

$2 \log _3 e$

Explanation:

Using Mean Value Theorem, we have

$f^{\prime}(c)=\frac{f(3)-f(1)}{3-1} \Rightarrow \frac{1}{c}=\frac{1}{2}\{\log 3-\log 1\} \Rightarrow c=2 \log _3 e$