Theorem and Explanations

Related lectures (29)

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Explores the conditions for a function to be continuous and differentiable.

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

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

Explores inflection points in functions, emphasizing the role of the second derivative.

Discusses conditions for functions to be strictly increasing or decreasing based on the derivative.

Covers continuity, differentiability, and applications in calculus with an emphasis on fundamental concepts.

Discusses the error between f'(x0) and its approximation using a backward finite difference formula.

Explores Rolle's Theorem for continuous and differentiable functions on closed intervals.

Covers primitive functions, infinite primitives, the theorem on primitives, and examples of indefinite integrals.

Introduces higher derivatives and the Taylor development, illustrating examples and discussing the uniqueness of the Taylor polynomial.