Lectures related to Rolle's Theorem: Applications and Examples

Tangent to Graph of a Function

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

The Intermediate Value Theorem

Explains the Intermediate Value Theorem for continuous functions on closed intervals.

Rolle's Theorem and Mean Value Theorem

Covers Rolle's Theorem and the Mean Value Theorem with illustrative examples.

Rolle's Theorem and Mean Value Theorem

Covers Rolle's Theorem and the Mean Value Theorem, demonstrating their applications through examples.

Rolle's Theorem

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

Differentiable Functions and Lagrange Multipliers

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

General Mathematics I: Derivatives and Tangents

Explores derivatives, tangents, and elementary function rules in general mathematics.

The Increment Theorem: Understanding Derivatives

Explores the increment theorem and derivatives in calculus, focusing on polygonal valleys and curve traces.

Differentiability of Functions of Several Variables

Covers the differentiability of functions of multiple variables and the significance of directional derivatives and gradients.

Continuity and Differentiability of Functions

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

Derivatives and Continuity in Multivariable Functions

Covers derivatives and continuity in multivariable functions, emphasizing the importance of partial derivatives.

Surjectivity of Derivative Application

Covers the surjectivity of the derivative application for continuous functions on closed intervals.

Derivability and Chain Rule

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

Derivatives and Continuity in Mathematics

Covers derivatives, continuity, Rolle's Theorem, function examples, and extrema.

Differential Calculation: Trigonometric Derivatives

Explores trigonometric derivatives, composition of functions, and inflection points in differential calculation.

Advanced Analysis II: Tangent Plan and Differentiability

Explores tangent planes and differentiability in advanced analysis, emphasizing the properties of tangent planes and the conditions for differentiability.

Theorem of Generalized Mean Value: Study of Functions

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

Advanced Analysis: Differential Equations Overview

Covers the fundamentals of differential equations, their properties, and methods for finding solutions through various examples.

Extreme Values Theorem

Discusses the Extreme Values Theorem for continuous functions on closed intervals.

Derivatives and Approximations: Logarithmic Functions

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