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?

Question

anonymous · Answer

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

jamesj · Answer

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.

anonymous · Answer

so this is true