Lecture

Derivability on an Interval: Rolle's Theorem

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In course

MATH-101(g): Analysis I

Étudier les concepts fondamentaux d'analyse et le calcul différentiel et intégral des fonctions réelles d'une variable. ...

Description

This lecture covers the concept of derivability on an interval, including Rolle's Theorem, finite increments, and Bernoulli-L'Hopital rule. It explains the conditions for a function to be derivable on a closed interval, with examples such as exponential and trigonometric functions. The lecture progresses to discuss the implications of derivability on both sides of a point within an interval, leading to the definition of derivability on a closed interval. It also introduces the concept of right and left derivability at a point within an interval, emphasizing the importance of limits in determining derivability. The lecture concludes with a detailed explanation of Rolle's Theorem and its application in determining specific points within a function.

Instructors (2)

Annalisa Buffa

Teaching & PhD PhD Students Gonzalo Bonilla Moreno, Philipp Christoph Weder, Yannis Dirk Voet, Fabio Marcinno, Ferhat Sindy, Francesco Sala, Markus Renoldner, Mohamed Ben Abdelouahab, Davor Dobrota Past EPFL PhD Students Luca Coradello, Ondine Chanon, Riccardo Puppi Courses Numerical approximation of PDEs MATH-451 The course is about the derivation, theoretical analysis and implementation of the finite element method for the numerical approximation of partial differential equations in on

Lénaïc Chizat

Teaching & PhD PhD Students Javier Esteban Maass Martinez Past EPFL PhD Students Guillaume Yitian Wang Courses Computational optimal transport MATH-528 Computational aspects of measure transportation, from classical optimal transport to modern denoising diffusion models. Topics in machine learning MATH-520 Mathematical analysis of modern supervised machine learning techniques, with an emphasis on the mathematics of artificial neural networks.

Official source

Ontological neighbourhood

Mathematics

Analysis: Calculus

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