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Questions  

 The function f(x)=(x1)|x1|+sin(|x|) is 

a
differentiable for all x∈R−{1}
b
discontinuous at x=1
c
differentiable for all x∈R−{0}
d
differentiable for all x

detailed solution

Correct option is C

Functions in |x| is not differentiable at x=0 but x x is differentiable ∀x Function (x−1)|x−1| is differentiable at all points.  So, function f(x)=|x−1|(x−1)+sin⁡|x| is not differentiable at x=0 only.

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