MathAnalysisCalculusMultivariable calculus

Partial derivatives

The hills

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What could be said about the function $f(x,y)$ at the point $(0, 0)$ ? Graph in three-dimensional space

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\dfrac{\partial f}{\partial x}(0, 0) = 0

\dfrac{\partial f}{\partial y}(0, 0) = 0

\dfrac{\partial f}{\partial x}(0, 0) > 0

\dfrac{\partial f}{\partial y}(0, 0) > 0

\dfrac{\partial f}{\partial x}(0, 0) > 0

\dfrac{\partial f}{\partial y}(0, 0) < 0

\dfrac{\partial f}{\partial x}(0, 0) = 0

\dfrac{\partial f}{\partial y}(0, 0) < 0

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