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Math Help - 3 times differentiable, but not 3 times continuously differentiable?

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    3 times differentiable, but not 3 times continuously differentiable?

    Does anyone know an example of a function that is 3 times differentiable, but not 3 times continuously differentiable?
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    Quote Originally Posted by paupsers View Post
    Does anyone know an example of a function that is 3 times differentiable, but not 3 times continuously differentiable?
    Try 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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