## anonymous 4 years ago If mixed partial derivatives are the same, this means that functions of this derivatives are continuous. Does this mean that also a function f is continuous in the same point?

1. anonymous

So, if derivatives are continuous in some point , there must be continuous also function?

2. JamesJ

If the partial derivatives of a function $f : \mathbb{R}^n \rightarrow \mathbb{R}^m$ exist and are continuous at a point p, then the function is differentiable at p. If the function f is differentiable at p, then it is continuous at p.

3. anonymous

so this is true