Calculus

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Surface contour curves of a saddle surface.

Saddle surface with its contour plot, showing increasing and decreasing gradients of g(x,y). The surface curves upward along one axis and downward along the other, demonstrating a critical point in the middle.

This illustration presents the saddle surface in three dimensions, accompanied by its contour plot in the xy-plane. The saddle surface exhibits regions of increasing and decreasing behavior, forming a critical point where it curves upward along one axis and downward along another. The surface plot shows the saddle’s hyperbolic shape, while the contour plot below indicates how the values of the function g(x, y) change, highlighting increasing and decreasing gradients along distinct directions.

This diagram is ideal for multivariable calculus and differential geometry textbooks, illustrating key concepts such as saddle points, critical points, contour plots, and partial derivatives.

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