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Lecture
Inflection Points
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Chapter 5: Function Studies
Covers the study of functions, including limits, derivatives, and sign variations.
Implicit Functions Theorem
Covers the Implicit Functions Theorem, explaining how equations can define functions implicitly.
Convexity and Concavity: Inflection Points, Taylor Expansion, and Darboux Sums
Explores inflection points, convexity, concavity, and asymptotes in functions, with examples and applications.
Function Studies: Limits, Derivatives, and Convexity
Covers the essential elements for studying a function, including its domain, behavior at boundaries, limits, derivatives, and points of inflection.
Partial Derivatives: Derivability
Explores partial derivatives and derivability of functions, emphasizing geometric interpretations and avoiding common pitfalls.
Differential Calculus: Definition and Derivability
Explores the definition and derivability of functions in differential calculus, emphasizing differentiability at specific points.
Rolle's Theorem: Applications and Demonstrations
Covers the applications and demonstrations of Rolle's Theorem in differential calculus.
Derivatives and Convexity
Explores derivatives, local extrema, and convexity in functions, including Taylor's formula and function compositions.
Convergence Criteria: Necessary Conditions
Explains necessary conditions for convergence in optimization problems.
Taylor's Formula: Developments and Extrema
Covers Taylor's formula, developments, and extrema of functions, discussing convexity and concavity.