Lectures related to Derivative test

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

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

Covers Riemann sums, definite integrals, Taylor series, and exponential of complex numbers.

Explains necessary conditions for convergence in optimization problems.

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

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

Explores inflection points in functions, emphasizing the role of the second derivative.

Explores determining local maximums, minimums, and inflection points of functions.

Explores inflection points, convexity, concavity, and asymptotes in functions, with examples and applications.

Explains the Jacobian matrix and derivative of composite functions with examples.

Covers Fermat's theorem, necessary optimality conditions, convexity, and eigenvalue curvature in optimization.

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

Explores exact linearization techniques for transforming non-linear systems into linear ones, emphasizing system stability.

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

Explores differential calculation with hyperbolic functions and Taylor series, emphasizing the importance of signed areas in integrals.

Covers higher derivatives, local extrema, and the application of Rolle's and Mean Value Theorems.

Explains partial derivatives, generalization, and second order derivatives with examples and mathematical notations.

Introduces higher derivatives and the Taylor development, illustrating examples and discussing the uniqueness of the Taylor polynomial.

Discusses the continuity of the derivative function and presents a counterexample of a function that is not necessarily continuous.

Explores the derivative of a function, covering rules for deriving sums, products, and quotients.