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

1. ## 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?

2. 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.