Lokální extrémy funkce, Lagrangeovy multiplikátory

Lokální extrém funkce dvou proměnných
[sup]Předpokládejme, že je plocha zadána diferencovatelnou funkcí [color=#0000ff][i]z = f(x,y)[/i][/color].[br]Nutnou podmínku, aby regulární plocha [color=#0000ff][i]z = f(x,y)[/i][/color] měla v bodě T lokální extrém je vodorovná tečná rovina. [url=https://cs.wikipedia.org/wiki/Gradient_(matematika)]Gradient[/url] plochy v regulárním bodě T musí být nulový vektor.[br][br][size=150]Vázané extrémy[/size][br]Pokud nás nezajímá jen samotný extrém funkce [color=#0000ff][i]z = f(x,y)[/i][/color], ale omezíme definiční obor v rovině (x,y) nějakou další vazební podmínkou, mluvíme o vázaných extrémech. Rovnice [color=#0000ff][i]y = v(x)[/i][/color] je řídící křivkou obecné válcové plochy, která je tvořena přímkami rovnoběžnými s osou [i]z[/i]. Extrémy hledáme na průnikové křivce válce [color=#0000ff][i]y = v(x)[/i][/color] a plochy [color=#0000ff][i]z = f(x,y)[/i][/color].[br][br]Složitější je hledání extrému funkce vázaných nějakou další podmínkou [color=#0000ff][i]g(x,y) = 0[/i][/color], kterou nelze zadat explicitně nebo parametricky. Nejznámější metodou, jak nalézt takové vázané extrémy, je [url=https://cs.wikipedia.org/wiki/Metoda_Lagrangeov%C3%BDch_multiplik%C3%A1tor%C5%AF]metoda Lagrangeových multiplikátorů[/url]. Geometrický princip je stejný: Podmínka [color=#0000ff][i]g(x,y) = 0[/i][/color] určuje řídící křivku válcové plochy s vertikálními přímkami. Průnikem válcové plochy [color=#0000ff][i]g(x,y) = 0[/i][/color] a plochy [color=#0000ff][i]z = f(x,y)[/i][/color] je křivka [i][color=#0000ff]k[/color][/i] a na ni hledáme extrém. Takový extrém bude právě v bodě, kde se křivka [i][color=#0000ff]k[/color][/i] dotýká nějaké vrstevnice plochy [color=#0000ff][i]z = f(x,y)[/i][/color], tedy vektory gradientů budou lineárně závislé [img]https://wikimedia.org/api/rest_v1/media/math/render/svg/660e2ed1096d19b66eb08c93334b963af3445878[/img].[br][/sup]
Užití Lagrangeových multiplikátorů
Najděte minimum funkce [color=#0000ff][i]z = xy[/i][/color] za podmínky dané rovnicí [i][color=#0000ff]c:[/color] [math]x^2-3xy+y^2=20[/math][/i].
[size=100][size=85]Označme funkci zadávající plochu [color=#0000ff][i]z[/i] = f([i]x, y[/i])[/color] a omezující vazbu [i][color=#0000ff]g(x, y) = 0[/color][/i].[br]Sestrojme Lagrangeovu funkci[color=#0000ff] L([i]x, y)[/i] =[/color] [color=#0000ff]f([i]x, y[/i])[/color] - λ [i][color=#0000ff]g(x, y) [/color][/i][br]Stacionární bod Lagrangeovy funkce: [color=#0000ff]L'[sub]x[/sub] ([i]x, y) = [/i]0 [color=#000000]a[/color][/color][color=#0000ff] L'[sub]y[/sub] ([i]x, y) = [/i]0[/color] je bod podezřelý z extrému.[br][br]Na hyperbolickém paraboloidu [color=#0000ff][i]z[/i] = [i]x . y [/i][color=#000000]a hyperbole [/color][/color][color=#0000ff]x[sup]2[/sup] [code]−[/code] 3xy + y[sup]2[/sup]= 20 [color=#000000]máme Langrangeovu funkci[br] [br][/color][/color][color=#0000ff]L([i]x, y)[/i] =[/color] [color=#0000ff][i]x . y[/i][/color] - λ [i][color=#0000ff]([color=#0000ff]x[sup]2[/sup] [code]−[/code] 3xy + y[sup]2[/sup] [i][color=#0000ff][color=#0000ff][code]−[/code] [/color][/color][/i]20[/color])[br][/color][/i][color=#0000ff][color=#000000][br]Hledáme stacionární bod[br][br][color=#0000ff]L'[sub]x[/sub] ([i]x, y) = y [/i][/color][/color][/color][color=#0000ff][color=#000000][color=#0000ff][i][i][color=#0000ff][color=#0000ff][code]−[/code] [/color][/color][/i] 2λx + 3[/i][/color][/color][/color][color=#0000ff][color=#000000][color=#0000ff][i][color=#0000ff][color=#000000][color=#0000ff][i]λ[/i][/color][/color][/color]y = [/i]0 [color=#000000]a [/color][/color][color=#0000ff]L'[sub]y[/sub] ([i]x, y) [color=#0000ff][color=#000000][color=#0000ff][i]= x + [/i][/color][/color][/color][color=#0000ff][color=#000000][color=#0000ff][i]3λx [i][color=#0000ff][color=#0000ff][i][color=#0000ff][color=#0000ff][code]−[/code][/color][/color][/i][/color][/color][/i] 2[color=#0000ff][color=#000000][color=#0000ff][i]λ[/i][/color][/color][/color]y[/i][/color][/color][/color] = [/i]0[br][/color][br]Nepřehlédnutelnou komplikací této metody je, že nám přibyla další neznámá - multiplikátor [color=#0000ff][color=#000000][color=#0000ff][i][color=#0000ff][color=#000000][color=#0000ff][i][color=#0000ff][color=#000000][color=#0000ff][i]λ[/i][/color][/color][/color][/i][/color][/color][/color][/i][/color][/color][/color]. Úpravame se snažíme jej vyloučit z hledané vazby. V našem případě toho dosáhneme, sečteme-li obě rovnice a vytkneme člen [color=#0000ff]([i]x+y[/i])[/color]. [br][color=#0000ff][color=#000000][color=#0000ff]([i]x+y[/i])[/color][/color][/color][color=#0000ff][color=#000000][color=#0000ff]([i]1+[color=#0000ff][color=#000000][color=#0000ff][i][color=#0000ff][color=#000000][color=#0000ff][i][color=#0000ff][color=#000000][color=#0000ff][i]λ[/i][/color][/color][/color][/i][/color][/color][/color][/i][/color][/color][/color][/i])=0[/color][/color][/color][br]Odtud máme jednoduchou vazbu pro extrémy nad hyperbolou: [color=#0000ff]x = [i][i][i][i][code]−[/code][/i][/i][/i][/i] y[/color]. Dosazením do hyperboly získáme souřadnice extrémů.[br]Funkce [i][color=#0000ff]z = x.y[/color][/i] má dvě minimální hodnoty nad hyperbolou: v bodech [color=#0000ff]Min1 = ([color=#0000ff][color=#000000][color=#0000ff][i][i][i][i][code]−[/code][/i][/i][/i][/i][/color][/color][/color]2, 2)[/color] a [color=#0000ff]Min2 = (2, [/color][/color][/color][color=#0000ff][color=#000000][color=#0000ff][color=#0000ff][color=#000000][color=#0000ff][i][i][i][i][code]−[/code][/i][/i][/i][/i][/color][/color][/color]2)[/color]. [/color][/color][/size][/size]
Úloha na vázaný extrém (Calculus 1)
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[/img]
Calculus 1 : Cvičení 12.1 [url=http://euler.fd.cvut.cz/predmety/Calculus1/index.html]Globální extrémy[/url]

Information: Lokální extrémy funkce, Lagrangeovy multiplikátory