Convexity and Concavity

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Related lectures (31)

Page 3 of 4

Convergence Criteria: Necessary Conditions

Explains necessary conditions for convergence in optimization problems.

Differentiable Functions and Lagrange Multipliers

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

Directional Derivatives

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

Implicit Examples: Hyperplane and Stationary Points

Illustrates finding hyperplanes for surfaces and determining stationary points.

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Optimization: Stationary Points and Local Extrema

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

Concavity and Convexity: Analysis of Functions

Explores concavity, convexity, critical points, and singularities in functions.

Application of Taylor's approximation formula

Covers the application of Taylor's formula, including composition of functions and detecting local extrema.

Taylor's Formula: Convexity, Inflection Points

Explores Taylor's formula, uniqueness of Taylor series, Mean Value Theorem, inflection points, and convexity.

Nature of Extremum Points

Explores the nature of extremum points in functions of class e² around the point (0,0), emphasizing the importance of understanding their behavior in the vicinity.