1sir, i have another opinion.
the analogy with x|x| does not hold as it is differentiable as can be seen
however, when cosx|x| is seen
we find it is NOT differentiable at x=0.
Thank you
Statement 1:
f(x) = \left | x \right |cosx is NOT differentiable at x=0
Statement 2:
Every Absolute value functions are NOT differentiable.
EXPLAIN YOUR ANSWER.
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66Statement 1 is true. Statement 2 is not true. Consider for example |x|x.
1
106A/R's usually imply that exceptions should not be there.. Even if there is a single exception then the statement becomes false
106lxlcosx is non differentiable at x=0
but what's the problem?
xlxl is differentiable every where..
So statement 2 is FALSE