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(A) $1$. For $f(x) = x^{1/3}$,the function is defined for all $x \in \mathbb{R}$. It is continuous everywhere. However,$f'(x) = \frac{1}{3}x^{-2/3} =

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$f(x) = x^{1/3}$

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(A) $1$. For $f(x) = x^{1/3}$,the function is defined for all $x \in \mathbb{R}$. It is continuous everywhere. However,$f'(x) = \frac{1}{3}x^{-2/3} = \frac{1}{3x^{2/3}}$. At $x = 0$,$f'(x)$ is undefined,so it is not differentiable at $x = 0$.$2$. For $f(x) = \frac{|x|}{x}$,the function is not defined at $x = 0$,so it is not continuous everywhere in its domain.$3$. For $f(x) = e^{-x}$,the function is continuous and differentiable everywhere.$4$. For $f(x) = 	an x$,the function is not defined at $x = (2n+1)\frac{\pi}{2}$,so it is not continuous everywhere in its domain.Thus,the correct option is $A$.

Which one of the following functions is continuous everywhere in its domain but has at least one point where it is not differentiable?

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