Calculus

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Local and global maximum and minimum points on a 3D surface.

3D surface with labeled local maximum, local minimum, global maximum, and global minimum points. The diagram illustrates the difference between local and global extrema in a function of two variables, showing critical points where the surface reaches peaks and valleys.

This 3D surface plot showcases the concepts of local and global extrema—including local maximum, local minimum, global maximum, and global minimum—as applied to a multivariable function. It serves as a visual aid for understanding the behavior of functions in three dimensions and the differentiation between local extrema (occurring within small neighborhoods) and global extrema (the absolute highest or lowest values over the entire surface).

Ideal for calculus, multivariable calculus, optimization courses, and machine learning contexts to explain critical points and optimization techniques.

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