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The value of c in Lagranges theorem for ...

The value of `c` in Lagranges theorem for the function `f(x)=logsinx` in the interval `[pi/6,(5pi)/6]` is `pi/4` (b) `pi/2` `(2pi)/3` (d) none of these

A

0

B

`(pi)/4`

C

`(pi)/2`

D

`(pi)/3`

Text Solution

Verified by Experts

The correct Answer is:
C
Given `f(x)=log sin x=f'(x)=cot x`
Put `f'(c)=0`
`impliescot c=0`
`impliesc=(pi)/2`
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