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Let K be the set of all real values of x...

Let K be the set of all real values of x where the function `f(x)=sinabsx+2(x-pi)cosabsx` is not differentiable. Then the set K is equal to

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The correct Answer is:
0
Only critical point is `x =0`
` x lt 0 f (x) =- sin x +x + 2 ( x - pi) cos x`
`L.H.D. f (x) =-cos x +1 +2 cos x -2 (x - pi) sin x`
`f ('O') =-1 +1+2=2`
`x gt 0 f (x) = sin x-x + 2( x-pi) cos x`
`f(x) =cos x -1 + 2 cos x-2 (x-pi) sin x`
`f ('O') =2`
L.H.D. = R. H.D.
`therefore fx` is differentiable everywhere.
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