Surface z = xy
Equation: z = x * y
z = xy is linear in each variable when the other is held fixed. A 45° rotation turns it into (u² − v²)/2, a saddle.
It is the first textbook example of a mixed partial: ∂²z/∂x∂y = 1.
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z =
Equation: z = x * y
z = xy is linear in each variable when the other is held fixed. A 45° rotation turns it into (u² − v²)/2, a saddle.
It is the first textbook example of a mixed partial: ∂²z/∂x∂y = 1.