👉 The term "besmoothed" in the context of mathematical analysis refers to a function that is smooth at all points where it is defined, but fails to be continuous at those same points. In other words, if you have a function $f(x)$ that is continuous everywhere except at one point $x_0$, then the derivative $f'(x_0)$ does not exist. This means that there are no values of $x$ such that $f'(x) =
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