Lecture

Extreme Absolute Points: Examples

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In course

MATH-106(f): Analysis II

Étudier les concepts fondamentaux d'analyse et le calcul différentiel et intégral des fonctions réelles de plusieurs variables. ...

Description

This lecture covers examples of absolute extrema, focusing on determining unique extreme points and the nature of stationary points. Through various examples, the instructor explains how to find extreme points and analyze the nature of stationary points in a given function.

Instructors (3)

Boris Buffoni

Research activityResearch ResearchCurrent Research Fields https://sma.epfl.ch/~buffoni/home.html Teaching & PhD Courses Analysis II MATH-106(b) The course studies fundamental concepts of analysis and the calculus of functions of several variables. Evolutional partial differential equations MATH-421 Fundamental techniques and theories for partial differential equations of evolution. Application to basic examples: first-order equations, wave equation, heat equation. The Cauchy

David Valentin Strütt

Assistanat Vous visitez cette page dans l'optique de rejoindre mon équipe d'asssistant·es pour un de mes cours d'analyse ? Vous trouverez plus d'informations ici. Contributions auteur de polycopiés d'analysecréateur matheminecraftrecord suisse du plus grand nombre de participations à la construction d'un additionneur binaire en dominos (autoproclamé) Je suis né pile le jour de mon anniversaire. Expériences professionnelles Chargé de communication pour MATH et chargé de cours pour la SMA 2019–2024 EPFLCharg

Adélie Eliane Garin

Teaching & PhD Courses Sustainability ENV-101 This course presents global sustainability issues. It introduces planetary boundaries, their systemic interconnections and social justice issues. The interdisciplinary approach introduces group work and systems thinking (interdependencies in a complex system). Sustainability in my research ENG-650 This course is designed to develop the necessary transversal skills to foster sustainability integration in the present and future rese

Official source

Related concepts (32)

Stationary point

In mathematics, particularly in calculus, a stationary point of a differentiable function of one variable is a point on the graph of the function where the function's derivative is zero. Informally, it is a point where the function "stops" increasing or decreasing (hence the name). For a differentiable function of several real variables, a stationary point is a point on the surface of the graph where all its partial derivatives are zero (equivalently, the gradient is zero).

Fermat's theorem (stationary points)

In mathematics, Fermat's theorem (also known as interior extremum theorem) is a method to find local maxima and minima of differentiable functions on open sets by showing that every local extremum of the function is a stationary point (the function's derivative is zero at that point). Fermat's theorem is a theorem in real analysis, named after Pierre de Fermat. By using Fermat's theorem, the potential extrema of a function , with derivative , are found by solving an equation in .

Maximum and minimum

In mathematical analysis, the maximum and minimum of a function are, respectively, the largest and smallest value taken by the function. Known generically as extremum, they may be defined either within a given range (the local or relative extrema) or on the entire domain (the global or absolute extrema) of a function. Pierre de Fermat was one of the first mathematicians to propose a general technique, adequality, for finding the maxima and minima of functions.

Inflection point

In differential calculus and differential geometry, an inflection point, point of inflection, flex, or inflection (rarely inflexion) is a point on a smooth plane curve at which the curvature changes sign. In particular, in the case of the graph of a function, it is a point where the function changes from being concave (concave downward) to convex (concave upward), or vice versa.

Definition

A definition is a statement of the meaning of a term (a word, phrase, or other set of symbols). Definitions can be classified into two large categories: intensional definitions (which try to give the sense of a term), and extensional definitions (which try to list the objects that a term describes). Another important category of definitions is the class of ostensive definitions, which convey the meaning of a term by pointing out examples. A term may have many different senses and multiple meanings, and thus require multiple definitions.

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