JEE Main 2007 — Application of Derivatives Question with Solution
JEE Main 2007
Question
A value of for which the conclusion of Mean Value Theorem holds for the function on the interval is
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Show full solutionCorrect option: A
Correct answer
A
Step-by-step explanation
Using mean value theorem
$\begin{aligned}
& f^{\prime}(c)=\frac{f(3)-f(1)}{3-1} \\
& \Rightarrow \frac{1}{c}=\frac{\log 3-\log 1}{2} \\
& \Rightarrow c=\frac{2}{\log _e 3}=2 \log _3 e.
\end{aligned}$
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This is a previous-year question from JEE Main 2007, covering the Application of Derivatives chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.