Limits Continuity And Differentiability Question 115
Question: If f(x) is differentiable everywhere, then which one of the following is correct?
Options:
A) $ | f | $ is differentiable everywhere except at points where $ f(x) = 0 $
B) $ {{| f |}^{2}} $ is differentiable everywhere
C) $ f| f | $ is not differentiable at some points
D) None of the above
Show Answer
Answer:
Correct Answer: C
Solution:
If f(x) is differentiable everywhere then |f| is not differentiable at some point, so, $ f|x| $ is not differentiable at some point.
[Example: f(x) = x is differentiable everywhere but |f(x)|= |x| is not differentiable at x = 0]
BETA
