Does anyone know an example of a function that is 3 times differentiable, but not 3 times continuously differentiable?
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Originally Posted by paupsers Does anyone know an example of a function that is 3 times differentiable, but not 3 times continuously differentiable? Try $\displaystyle f(x) = x^6\sin(1/x)$ (with f(0) = 0). The third derivative will exist everywhere but be discontinuous at the origin.
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