Extreme Points of Functions

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Related lectures (30)

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Implicit Function Theorem: Local Extrema

Explores the Implicit Function Theorem, local extrema, supporting hyperplanes, and higher-order derivatives.

Implicit Function Theorem

Explores the Implicit Function Theorem, supporting hyperplanes, local extrema, and higher-order derivatives, concluding with the classification of stationary points.

Optimization: Stationary Points and Local Extrema

Covers the concept of stationary points in optimization and how to identify local extrema.

Derivative and Local Extrema Study

Explores the study of local minima and maxima through derivatives and sign changes.

Convexity and Concavity: Inflection Points, Taylor Expansion, and Darboux Sums

Explores inflection points, convexity, concavity, and asymptotes in functions, with examples and applications.

Convergence Criteria: Necessary Conditions

Explains necessary conditions for convergence in optimization problems.

Implicit Examples: Hyperplane and Stationary Points

Illustrates finding hyperplanes for surfaces and determining stationary points.

Derivatives and Convexity

Explores derivatives, local extrema, and convexity in functions, including Taylor's formula and function compositions.

Partial Derivatives: Extrema and Hessians

Discusses extrema of functions with multiple variables and the hessian matrix.

General Case

Explores determining local maximums, minimums, and inflection points of functions.