Optimization: Stationary Points and Local Extrema

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Derivative and Local Extrema Study

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

Taylor's Formula: Developments and Extrema

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

Points 7-9 du procédé

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

Applications of Differential Calculus

Explores applications of differential calculus, including theorems, convexity, extrema, and inflection points.

Implicit Function Theorem: Local Extrema

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

Derivatives and Reciprocal Functions

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

Tangent to Graph of a Function

Explores finding the equation of the tangent line to a function's graph at a point.

Implicit Function Theorem

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

Convexity and Optimization

Explores convexity, optimization, and critical points in mathematical functions using the second derivative.

Euler-Lagrange Equations

Covers the derivation and application of Euler-Lagrange equations for optimization problems in mathematical analysis.