# 3 times differentiable, but not 3 times continuously differentiable?

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• Feb 6th 2010, 02:11 PM
paupsers
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?
• Feb 7th 2010, 12:18 AM
Opalg
Quote:

Originally Posted by paupsers
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.