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I. Differentiation – 6. Maksimum/minimum 134 Kantlængder for størst rumfang er Vxx(2,2) = −1, Vxy(2,2) = −1/2, Vyy(2,2) = −1 (a,b) V (a,b) Vxx(a,b) D(a,b) Type (2,2) 4 −1 3/4 maksimum (x,y,z) = (2,2,1) 6.36. Lukket mængde ☞ [S] 11.7 Maximum and minimum values Definition Givet en delmængde D ⊂ R 2 . Et punkt (a,b) er et randpunkt til D, hvis enhver cirkelskive med centrum i (a,b) og positiv radius indeholder punkter fra D samt punkter, der ikke ligger i D. Delmængden D er lukket, hvis ethvert randpunkt er med. Eksempel D = {(x,y)|x 2 + y 2 ≤ 1} har randpunkter {(x,y)|x 2 + y 2 = 1} og er lukket. 6.37. Randpunkt ☞ [S] 11.7 Maximum and minimum values Definition - figur
I. Differentiation – 6. Maksimum/minimum 135 y D randpunkt 6.38. Absolut ekstremum ☞ [S] 11.7 Maximum and minimum values 8 Sætning (Ekstrem værdi) Hvis f : D → R er kontinuert på en lukket og begrœnset delmœngde D ⊂ R 2 , så antager f både en absolut maksimumsvœrdi og en absolut minimumsvœrdi i punkter, der ligger i mœngden D. x
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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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1. Grafiske/numeriske metoder IV Di
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V. Matricer - 4. Determinanter 419
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V. Matricer - 4. Determinanter = (
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1. Egenvektorer VI Egenvektorer og
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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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