Consider the following two statements about the function $f(x)=\left\vert x\right\vert$:
Which of the following is TRUE?
ans is A. f(x)=|x| here for all values of x, f(x) exists. therefore it is continuous for all real values of x.
At x=0, f(x) is not differentiable. Because if we take the left hand limit here, it is negative while the right hand limit is positive.