Functions Question 339
Question: If $ f(x)=,|x| $ , then $ f(x) $ is
[DCE 2002]
Options:
A) Continuous for all x
B) Differentiable at $ x=0 $
C) Neither continuous nor differentiable at $ x=0 $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
It is obvious that $ |x| $ is continuous for all x. Now, $ R{f}’(x)=\underset{h\to 0}{\mathop{\lim }},\frac{|0+h|-0}{h}=1 $ $ L{f}’(x)=\underset{h\to 0}{\mathop{\lim }},\frac{|0-h|-0}{-h}=-1 $ Hence $ f(x)=,|x| $ is not differentiable at $ x=0 $ .
BETA
