A) Continuous for all x
B) Differentiable at \[x=0\]
C) Neither continuous nor differentiable at \[x=0\]
D) None of these
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 \[x=0\].
You need to login to perform this action.
You will be redirected in
3 sec
