Lectures related to Theorem and Explanations

Covers the demonstration of the chain rule and the theorem of Rolle.

Explores the connection between limit existence and function continuity, emphasizing derivative properties and function graphs.

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

Explores derivability, continuity, and composite functions with illustrative examples.

Covers the theory of finite differences and the mean value theorem.

Covers the derivative of the composition of two functions and the chain rule theorem.

Explores the theorems of continuity and derivative numbers, including strict monotonicity and the Newton ratio.

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

Explores finding the equation of the tangent line to a function's graph at a point.

Explores the practical applications of Rolle's Theorem in finding points where the derivative is zero.

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.