Question

A value of \( c \) for which conclusion of Mean Value Theorem holds for the function \( f(x) = \log x \) on the interval [1, 3] is

• A. \( \log 3 \)
• B. \( \log 2 \)
• C. \( \log 3 \)
• D. \( \frac{1}{\log 3} \)

Hint:

The Mean Value Theorem helps us find a point where the instantaneous rate of change equals the average rate of change over an interval.

Answer 1

The Correct Option is B

Step 1: Apply the Mean Value Theorem.
For the function \( f(x) = \log x \), the Mean Value Theorem applies when the derivative of the function equals the difference in function values divided by the interval length.
Step 2: Conclusion.
Thus, the correct value of \( c \) is \( \log 2 \).
Final Answer: \[ \boxed{\log 2} \]