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B
x=(nπ2),n∈Z
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C
x=2nπ,n∈Z
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D
x=nπ,nisanoddinteger
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Solution
The correct option is Ax=nπ,n∈Z f(x)=∣∣∣sinx∣∣∣⇒f(x)=(sinx,if2nπ<x<(2n+1)π−sinx,if(2n+1)π<x<(2n+2)π⇒f'(x)=(cosx,if2nπ<x<(2n+1)π−cosx,if(2n+1)π<x<(2n+2)πSo,f(x)isnotdifferentiableatx=...,0,π,2π,..Hence,∣∣∣sinx∣∣∣isnotdifferentiableforx=nπ,n∈Z