Lectures related to Implicit Function Theorem: Local Extrema

Implicit Function Theorem

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

Implicit Examples: Hyperplane and Stationary Points

Illustrates finding hyperplanes for surfaces and determining stationary points.

Derivative and Local Extrema Study

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

Optimization: Stationary Points and Local Extrema

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

Convergence Criteria: Necessary Conditions

Explains necessary conditions for convergence in optimization problems.

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

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

Differential Calculation: Trigonometric Derivatives

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

Derivatives and Convexity

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

Extreme Points of Functions

Covers the definition of extremum of a function and necessary conditions for local extrema.

General Case

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

Partial Derivatives: Extrema and Hessians

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

Optimization Techniques: Local and Global Extrema

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

Derivative and Local Extrema Study

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

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.

Taylor's Formula: Developments and Extrema

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

Rolle's and Mean Value Theorem

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

Chapter 5: Function Studies

Covers the study of functions, including limits, derivatives, and sign variations.

Optimality Conditions: Unconstrained

Covers Fermat's theorem, necessary optimality conditions, convexity, and eigenvalue curvature in optimization.

Points 7-9 du procédé

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