If `f(x)` is differentiable everywhere, then which one of the following is correct?

Options

A. `|f|` is differentiable everywhere
B. `|f|^(2)` is differentiable everywehere
C. `f|f|` is not differentiable at some points
D. None of the above

Answer

C

Explanation

If f(x) is differential everywhere then `|f|` is not differentiable at some point, so, `f|f|` is not differentiable at some point.
[Example: f(x)=x is differentiable everywhere but `|f(x)|=|x|` is not differentiable at x=0]