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If f(x)=|sinx-|cosx||, then the value of...

If `f(x)=|sinx-|cosx||,` then the value of `f^(')(x)` at `x=(7pi)/6` is

A

positive `y`-axis and positive `y`-axis respectively

B

`(1-sqrt(3))/2`

C

`0`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
In the neighborhood of `x=(7pi)/6`, we have `f(x)=|sinx+cosx|=-sinx-cosx`
`:.f^(')(x)=-cosx+sinx, f^(')((7pi)/6)=-cos((7pi)/6)+sin((7pi)/6)`
`f^(')((7pi)/6)=(sqrt(3)-1)/2`
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