Lectures related to Continuous Functions: Derivability and Global Properties

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

Covers the theorems on continuous functions and extremums in compact sets.

Introduces and summarizes differential calculus, covering continuous functions, limits, differentiability, and tangent planes.

Covers the conditions for finding absolute extrema in multivariable functions.

Explores derivatives and approximations, focusing on logarithmic functions and their properties.

Covers derivatives, reciprocal functions, Rolle's theorem, and extremum local concepts.

Covers extreme values of continuous functions on compact sets and differentiability.

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

Discusses optimization techniques, focusing on local and global extrema in functions.

Covers the Mean Value Theorem in differential calculus, focusing on critical points and global extrema within intervals.

Covers differentiable functions, extreme points, and the Lagrange multiplier method for optimization.

Explains how a function reaches its maximum and minimum values.

Covers linear approximation, parametric derivatives, and differentiability conditions on intervals.

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

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

Explores differentiability, partial derivatives, Schwarz's theorem, and function continuity in mathematical analysis.

Explains partial derivatives, Hessienne matrix, and their properties.

Explores the Local Inversion Theorem and extremum points in functions.

Covers the theorem of intermediate values and finding maximum and minimum values of functions on closed intervals.

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