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If a function $\mathbb{R} \to \mathbb{R}$ is continuous or derivable at a point $x_0$ of its domain, is also continuous or derivable in a neighbourhood of $x_0$ ?

Git Gud
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halfpog
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    http://www.math.tamu.edu/~tvogel/gallery/node4.html – Git Gud Nov 28 '15 at 11:50
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    A function that is continuous at precisely one point: http://math.stackexchange.com/questions/60050/find-a-function-f-mathbbr-to-mathbbr-that-is-continuous-at-precisely-o. A function that is differentiable at precisely one point: http://math.stackexchange.com/questions/108388/function-which-is-continuous-everywhere-in-its-domain-but-differentiable-only-a. – Martin R Nov 28 '15 at 11:52

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