Nature of Extremum Points

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Covers Taylor approximation and extrema in multivariable functions with examples.

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Revisits local and absolute extremums of multivariable functions, emphasizing critical points and their classification.

Discusses optimization techniques, focusing on local and global extrema in functions.

Covers the discussion of local extrema, concavity, convexity, and inflection points in functions.

Covers the classification of stationary points in functions of two variables using the Hessian matrix.

Explores the diagonalization of matrices through eigenvalues and eigenvectors, emphasizing the importance of bases and subspaces.

Covers the theory and examples of diagonalizing matrices, focusing on eigenvalues, eigenvectors, and linear independence.

Covers differentiable functions, extreme points, and the Lagrange multiplier method for optimization.

Explores the Local Inversion Theorem and extremum points in functions.