The following scalar field is given: \(V(x, y, z)=2 x^{2}+x y z+y\). Verify that Schwarz's theorem is satisfied.

Schwarz's theorem:

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Mention should now be made of an important theorem of Mathematical Analysis, the Schwarz's Theorem, which states that (under appropriate assumptions) the order in which the partial derivatives are performed in a mixed derivative of a function with real variables is irrelevant. The appropriate assumptions are practically always verified in the physical cases of interest. Formally, Schwarz's theorem states that (using Cartesian coordinates) for a function V(x, y, z): a av (BY) = x (6) (6.45)