Lectures related to Extreme Points of Functions

Implicit Function Theorem: Local Extrema

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

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.

Rolle's and Mean Value Theorem

Covers higher derivatives, local extrema, and the application of Rolle's and Mean Value Theorems.

Derivative and Local Extrema Study

Explores the study of local extrema using derivatives and the importance of continuity at critical points.

Optimization Techniques: Local and Global Extrema

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

Taylor's Formula: Developments and Extrema

Covers Taylor's formula, developments, and extrema of functions, discussing convexity and concavity.

Differential Calculation: Trigonometric Derivatives

Explores trigonometric derivatives, composition of functions, and inflection points in differential calculation.

Derivatives and Reciprocal Functions

Covers derivatives, reciprocal functions, Rolle's theorem, and extremum local concepts.

Directional Derivatives

Explores directional derivatives in two-variable functions and extremum points.

Partial Derivatives: Taylor Formula

Explores partial derivatives, Taylor formula, examples, and extrema of functions.

Points 7-9 du procédé

Covers the analysis of local and global extrema, concavity, and inflection points.

Convexity Study and Limiting Developments

Explores convexity, concavity, and limiting developments for functions, emphasizing extrema and derivative properties.