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?

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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?

Mathematics
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So, if derivatives are continuous in some point , there must be continuous also function?
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.
so this is true

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