Lectures related to Derivative and Variation

Explores derivatives, local extrema, and function variation in mathematical analysis.

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

Covers the Mean Value Theorem, l'Hopital rule, Taylor's approximation, and more.

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

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

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

Explores Rolle's Theorem and its corollaries, including applications and proofs.

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

Covers the concepts of convexity and concavity in functions with examples.

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

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

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

Explores invertible matrices, injective functions, and the theory of reciprocal functions.

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

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

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

Covers partial derivatives for functions of one and two variables, emphasizing their importance and calculation.

Explores reciprocal functions, strict monotonicity, and continuity in advanced analysis.

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

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