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.