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.
Ref: http://math.stackexchange.com/questions/991475/why-is-the-absolute-value-function-not-differentiable-at-x-0
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