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I. Differentiation – 7. Lagrangemetoden 142 ✌ Flere bindinger ✌ August 2000, opgave 7 7.2. Skitse ☞ [S] 11.8 Niveaukurver y g(x,y)=k Lagrange situation f(x,y)=1 7.3. Maksimum/minimum under bibetingelse ☞ [S] 11.8 Lagrange multipliers Lagrange Problem Bestem ekstremumspunkter for en funktion f(x,y), når samtidig ligningen g(x,y) = k er opfyldt. Ligningen g(x,y) = k kaldes undertiden begrœnsningen eller bibetingelsen. 0 1 2 3 2 x
I. Differentiation – 7. Lagrangemetoden 143 Hvis ligningen g(x,y) = k kan løses, y = φ(x), reduces problemet til ekstremum for den sammensatte funktion i 1 variabel x ↦→ f(x,φ(x)). Hvis løsningskurven til ligningen g(x,y) = k kan parametriceres med (x(t),y(t)), reduces problemet til ekstremum for den sammensatte funktion i 1 variabel t ↦→ f(x(t),y(t)). 7.4. Maksimum/minimum under bibetingelse ☞ [S] 11.8 Lagrange multipliers Eksempel Bestem ekstremumspunkter for funktionen når samtidig ligningen f(x,y) = x + 3y g(x,y) = x 2 + y 2 = 10 er opfyldt. Løsning Niveaukurverne for f er linjer x+3y = c. Ekstremum findes når disse tangerer cirklen x 2 +y 2 = 10. 7.5. Maksimum/minimum under bibetingelse ☞ [S] 11.8 Lagrange multipliers Eksempel - figur
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CALCULUS "SLIDES" TIL CALCULUS 1 +
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3. Generelle områder 201 4. Koordi
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I. Differentiation - 1. Kontinuitet
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Litteratur • Arnold, Ordinary dif
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0-række/søjle, 423 n-te afsnitssu
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Identitetsmatricen, 383 Identitetsm
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