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I. Differentiation – 7. Lagrangemetoden 146 7.9. Lagrange multiplikator metode ☞ [S] 11.8 Lagrange multipliers Ligninger Lagranges ligningssystem for bestemmelse af ekstremumspunkter for en funktion f(x,y) under begræsningen g(x,y) = k. fx(x,y) = λgx(x,y) fy(x,y) = λgy(x,y) g(x,y) = k 7.10. Multiplikator metode ☞ [S] 11.8 Lagrange multipliers Eksempel - igen Bestem ekstremumspunkter for funktionen f(x,y) = x + 3y, når samtidig ligningen g(x,y) = x 2 + y 2 = 10 er opfyldt. Lagrangeligningerne er 1 = λ2x 3 = λ2y x 2 + y 2 = 10
I. Differentiation – 7. Lagrangemetoden 147 7.11. Multiplikator metode ☞ [S] 11.8 Lagrange multipliers Eksempel - igen fortsat Der løses 3x = y og x 2 + (3x) 2 − 10 = 0 der giver Lagrange multiplikator er (x,y) = ±(1,3) λ = ± 1 2 7.12. Maksimum/minimum under bibetingelse ☞ [S] 11.8 Lagrange multipliers Lagrange Problem Bestem ekstremumspunkter for en funktion f(x,y,z), når samtidig ligningen g(x,y,z) = k er opfyldt. Ligningen g(x,y,z) = k kaldes undertiden begrœnsningen eller bibetingelsen. Hvis ligningen g(x,y) = k kan løses, z = φ(x,y), reduces problemet til ekstremum for den sammensatte funktion i 2 variabel f(x,y,φ(x,y)) 7.13. Lagranges multiplikator ☞ [S] 11.8 Lagrange multipliers
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CALCULUS "SLIDES" TIL CALCULUS 1 +
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3. Generelle områder 201 4. Koordi
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Forord "Slides" til forelæsningern
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I. Differentiation - 1. Kontinuitet
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Litteratur • Arnold, Ordinary dif
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