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Related lectures (30)

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Extrema of Functions

Covers the discussion of local extrema, concavity, convexity, and inflection points in functions.

Supporting Hyperplanes

Illustrates finding supporting hyperplanes for surfaces and determining stationary point nature.

Derivative and Local Extrema Study

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

Derivatives: Definition and Properties

Explores the definition and properties of derivatives, including slopes of tangent lines and differentiability conditions.

Derivative and Local Extrema Study

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

Differential Calculus: Definition and Derivability

Explores the definition and derivability of functions in differential calculus, emphasizing differentiability at specific points.

Implicit Function Theorem: Local Extrema

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

Taylor's Formula: Developments and Extrema

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

Implicit Function Theorem

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

Partial Derivatives: Derivability

Explores partial derivatives and derivability of functions, emphasizing geometric interpretations and avoiding common pitfalls.