Multivariable Derivative Test

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This Demonstration evaluates partial derivatives up to the second order for multivariate functions, as well as the discriminant . The geometric significance of the mixed partial derivatives and the discriminant is emphasized.


Use the first popup menu to select a function to investigate and the second popup menu to choose one of its derivatives or the discriminant.

The graphic shows a wire drawing of the selected function and a plane of level curves. The level curves are projected onto the - plane and you can adjust their height. Adjust the height of the plane below the surface or within its interior to better see the interaction between the surface and the selection.

The contours of the surface in conjunction with the level curves enable an interpretation of the significance of the derivative.

The sliders control the size of the square base, the density of the mesh on the surface, the height of the display and the position of the plane of level curves within the plot of the surface.


Contributed by: Carl McCarty (December 2020)
Open content licensed under CC BY-NC-SA



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