Differential calculus | Articles containing proofs | Theorems in real analysis | Theorems in calculus

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 . Fermat's theorem gives only a necessary condition for extreme function values, as some stationary points are inflection points (not a maximum or minimum). The function's second derivative, if it exists, can sometimes be used to determine whether a stationary point is a maximum or minimum. (Wikipedia).

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Determine Function from Stationary Points

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From playlist Applications of Differentiation

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Determining the nature of stationary points - Differentiation

Do some complex problems on differentiation finding stationary points and evaluating their nature by first derivative test.

From playlist Further Calculus - MAM Unit 3

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Understanding Stationary Points (3 of 3: Determining nature)

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From playlist Applications of Differentiation

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Stationary Points: Step-by-Step Guide

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From playlist Applications of Differentiation

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Understanding Stationary Points (2 of 3: Location)

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From playlist Applications of Differentiation

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L'équation du soir 6/6 - Roland Lehoucq - Univers Convergents 2018

Extrait de la séance sur le film "Premier Contact". Nouvelle année, nouvelle formule ! A chaque séance, le parrain ou marraine présente une formule mathématique en lien avec le film projeté durant la séance. Pour cette séance Roland Lehoucq nous présente une équation lumineuse ! Vous po

From playlist Ciné-Club Univers Convergents

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Snell's law part 1: Ray optics derivation

In this video, I show how to derive the scalar form of Snell's law of refraction, starting from the postulates of ray optics.

From playlist Two-part series on Snell's law

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Ch4 Pr10: Classifying Stationary Points

How to use the corollary to Taylor's Theorem to classify stationary points. Presented by Dr John Steele from the UNSW School of Mathematics and Statistics.

From playlist Mathematics 1B (Calculus)

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Is ACTION The Most Fundamental Property in Physics?

Learn More About NordVPN at: https://nordvpn.com/spacetime It’s about time we discussed an obscure concept in physics that may be more fundamental than energy and entropy and perhaps time itself. That’s right - the time has come for Action. Sign Up on Patreon to get access to the Space

From playlist The Standard Model Lagrangian Playlist

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The Abel Prize announcement 2016 - Andrew Wiles

0:44 The Abel Prize announced by Ole M. Sejersted, President of The Norwegian Academy of Science and Letters 2:07 Citation by Hans Munthe-Kaas, Chair of the Abel committee 8:01 Popular presentation of the prize winners work by Alex Bellos, British writer, and science communicator 21:43 Pho

From playlist The Abel Prize announcements

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Why was this visual proof missed for 400 years? (Fermat's two square theorem)

Today's video is about a new really wonderfully simple and visual proof of Fermat's famous two square theorem: An odd prime can be written as the sum of two integer squares iff it is of the form 4k+1. This proof is a visual incarnation of Zagier's (in)famous one-sentence proof. 0:00 Intr

From playlist Recent videos

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Alex Bellos on Andrew Wiles and Fermat's last theorem

Popular presentation by Alex Bellos on Sir Andrew Wiles and on Fermat's last theorem. This clip is a part of the Abel Prize Announcement 2016. You can view Alex Bellos own YouTube channel here: https://www.youtube.com/user/AlexInNumberland

From playlist Popular presentations

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Richard Pinch: Fermat's Last Theorem [1994]

Richard Pinch: Fermat's Last Theorem Based on the 1994 London Mathematical Society Popular Lectures, this special 'television lecture' entitled "Fermat's last theorem" is presented by Dr Richard Pinch. The London Mathematical Society is one of the oldest mathematical societies, founded i

From playlist Mathematics

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A Short Course in Algebra and Number Theory - Fermat's little theorem and primes

To supplement a course taught at The University of Queensland's School of Mathematics and Physics I present a very brief summary of algebra and number theory for those students who need to quickly refresh that material or fill in some gaps in their understanding. This is the fifth lectur

From playlist A Short Course in Algebra and Number Theory

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Fermat’s HUGE little theorem, pseudoprimes and Futurama

A LOT of people have heard about Andrew Wiles solving Fermat's last theorem after people trying in vain for over 350 years. Today's video is about Fermat's LITTLE theorem which is at least as pretty as its much more famous bigger brother, which has a super pretty accessible proof and which

From playlist Recent videos

Related pages

Monotonic function | Secant line | Exterior derivative | Zero of a function | Second derivative | Linear function | Pierre de Fermat | Derivative | Inflection point | Theorem | Differentiable function | Continuous function | Limit of a function | Domain of a function | Mean value theorem | Degree of a polynomial | Arg max | Boundary (topology) | Adequality | Stationary point | Differentiable manifold | Neighbourhood (mathematics) | Maxima and minima | Darboux's theorem (analysis) | Polynomial function | Equation | Real analysis | Mathematics | Set (mathematics) | Function (mathematics) | Critical point (mathematics) | Without loss of generality | Interval (mathematics)