Derivative and Linear Approximation

Related lectures (37)

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

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

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

Introduces the study of functions defined by power series and emphasizes the importance of separately considering boundary points.

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

Covers the derivative of the reciprocal function and its properties.

Explores Taylor series expansions for derivatives and integrals, including practical applications.

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

Explains definitions and remarks about closed intervals in functions.

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

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

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

Explores algebraic operations on limited developments and their consequences on differentiable functions, illustrated through examples.

Covers the definition of differentiable functions and explores the representation of the remainder in derivatives.

Explores the extension of the chain rule to higher dimensions and compositions of functions.

Covers derivatives, reciprocal functions, Rolle's theorem, and extremum local concepts.

Explores the connection between limit existence and function continuity, emphasizing derivative properties and function graphs.

Covers differentiable functions, derivatives, and tangent planes in mathematics.

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

Explains partial derivatives, Hessienne matrix, and their properties.

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