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> Let $n$ be a positive integer. Find a function $f$ over $\mathbb{R}$ that is $n$ times differentiable but $f^{(n)}$ is not continuous.
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We know that all the derivatives $f',f'',...,f^{(n-1)}$ are all continuous, but how do we find a function where the last derivative is not continuous? The function we make up can't have absolute values obviously, so I was thinking it is going to have to be piecewise.