A) \[\left| f \right|\] is differentiable everywhere
B) \[{{\left| f \right|}^{2}}\]is differentiable everywhere
C) \[f\left| f \right|\]is not differentiable at some points
D) None of the above
Correct Answer: C
Solution :
[c] If f(x) is differential everywhere then |f| is not differentiable at some point, so, \[f\left| \,x \right|\] is not differentiable at some point. [Example: f(x) = x is differentiable everywhere but |f(x)|= |x| is not differentiable at x = 0]
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