Figuratively speaking, the necessary and sufficient condition is that this binary function should be continuous and smooth. Imagine a smooth plane in a three-dimensional coordinate system, just like the water surface, without creases, and the second derivative of this function is equal.

When it is not equal, it is generally not smooth. For example, when two planes intersect on a straight line, the second-order partial derivatives are not equal on the intersection line. Of course, if a second derivative itself is meaningless, let alone.