APFIVE Differentiability of an Absolute Value Function
Consider the function $$f(x) = |x - 1|$$ at $$x = 1$$. Which of the following statements about $$f$$ is true?
A
$$f$$ is not continuous at $$x = 1$$.
B
$$f$$ is continuous at $$x = 1$$ but the left and right derivatives at $$x = 1$$ are not equal.
C
$$f$$ is differentiable at $$x = 1$$.
D
$$\displaystyle\lim\limits_{h \to 0^-} \frac{f(1 + h) - f(1)}{h} = \lim\limits_{h \to 0^+} \frac{f(1 + h) - f(1)}{h}$$
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