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If f(x) = |cos x - sin x| , " then " '(...

If ` f(x) = |cos x - sin x| , " then " '((pi)/(6)) ` is equal to

A

`(1)/(sqrt(2))`

B

1

C

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

D

`sqrt(3)`

Text Solution

Verified by Experts

The correct Answer is:
B
When ` 0 lt x lt (pi)(4) , "" cos x gt sin x, ` so that
` cos x - sin x gt 0 `
i.e. ` f(x) = cos x - sin x `
` f'(x) =- sin x - cos x `
Hence `f'((pi)/(6)) = - sin""(pi)/(6) - cos""(pi)/(6) = - (1)/(2) (1 + sqrt(3))`
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