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5. Continuity and Differentiation
medium
A value of $c$ for which conclusion of Mean Value Theorem holds for the function $f\left( x \right) = \log x$ on the interval $[1,3]$ is
A
$2{\log _3}e$
B
$\frac{1}{2}{\log _e}3$
C
$\;{\log _3}e$
D
${\log _e}3$
(AIEEE-2007)
Solution
$f^{\prime}(c)=\frac{f(b)-f(a)}{b-a}$
$=\frac{f(3)-f(1)}{3-1}$
$f^{\prime}(c)=\frac{\log _{e}^{3}-\log _{e}^{1}}{2}$
$\frac{1}{2} \log _{e}^{3} $
$\frac{1}{c}=\frac{1}{2} \log _{e} 3$
Standard 12
Mathematics
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