Lectures related to Derivability Study: Behavioral Rules and Examples

Real Functions: Definitions and Properties

Covers the definitions and basic properties of real functions, including domain, image set, notation, and graph.

Derivative and Function Variation

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

Derivatives and Continuity in Mathematics

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

Functions: Limits and Continuity

Explores functions, limits, continuity, differentiability, and important notions of limits and divergence.

Derivatives and Approximations: Logarithmic Functions

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

Immediate Consequences

Explores the immediate consequences of f' = 0 and monotonicity on intervals.

Demonstration of Theorem 8.2

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

Demonstration of Rolle's Theorem

Demonstrates how to use a specific function to prove Rolle's Theorem.

Functions Composition: Continuity & Elements

Covers the composition of functions, continuity, and elementary functions, explaining the concept of continuity and the construction of elementary functions.