Let $f(x) = |x|, x \in R$. Then, which of the following statements is incorrect? A). $f$ has a minimum value at $x = 0$ B). $f$ has no maximum value in $R$ C). $f$ is continuous at $x = 0$ D). $f$ is differentiable at $x = 0$

The correct answer is $f$ is differentiable at $x = 0$. $f(x)=|x|$ is continuous everywhere but not differentiable at $x=0$. Left derivative = -1, Right derivative = +1 Hence, derivative does not exist at 0.

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