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A value of C for which the coclusion of ...

A value of C for which the coclusion of mean value theorem holds for the function f(x) `log_(e)x` on the interval `[1,3]` is

A

`2 log_(3)e`

B

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

C

`log_(3)e`

D

`log_(e)3`

Text Solution

Verified by Experts

The correct Answer is:
A
Using Mean Value Theorem, we have
`f'(c)=(f(3)-f(1))/(3-1)rArr(1)/(c)=(1)/(2){log3-log 1} rArr c= log _(3)e`
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