Global and local extrema of functions

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Explores the Darboux theorem for continuous functions on closed intervals, emphasizing uniform continuity and function behavior implications.

Explores real functions, covering parity, periodicity, and polynomial functions.

Explores continuous functions and integrability through practical examples.

Explores limits, continuity, and uniform continuity in functions, including properties at specific points and closed intervals.

Explores the integration by parts technique through examples, showcasing its step-by-step application to functions like cos(x) and sin(x.

Explores the conditions for continuity and differentiability of functions on a closed interval.

Covers differentiability of functions in two variables and the conditions for a function to be differentiable.

Covers the method of Lagrange multipliers to find extrema subject to constraints.

Explores continuity, differentiability, boundedness, and extrema of functions in multiple variables.

Explains global and local maxima and minima of functions, with examples and a guarantee theorem.