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I. Differentiation – 6. Maksimum/minimum 122 har kritisk punkt ∇f(x,y) = (−2x,2y) = 0 ⇔ (x,y) = (0,0) f(x,0) < 0, f(0,y) > 0, (x,y) = 0 viser, at (0,0) ikke er et lokalt ekstremum, altså er (0,0) et saddelpunkt. 6.16. Ekstremumspunkt ☞ [S] 11.7 Maximum and minimum values Eksempel 2 - figur z x Saddelpunkt i (0,0) 6.17. 2. ordens kriterium ☞ [S] 11.7 Maximum and minimum values y
I. Differentiation – 6. Maksimum/minimum 123 Sætning - (en variabel) Antag den afledede Så gœlder (a) f ′′ (a) > 0 ⇒ a lokalt minimum (b) f ′′ (a) < 0 ⇒ a lokalt maksimum f ′ (a) = 0 6.18. 2. ordens kriterium, lokalt maksimum ☞ [S] 11.7 Maximum and minimum values En variabel - figur y lokalt maksimum x1 x2 f ′ (0)=0 f ′ (x1)>0 f ′ (x2)
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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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II. Integration - 1. Dobbelt integr
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III. Potensrækker - 4. Taylorpolyn
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1. Grafiske/numeriske metoder IV Di
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IV. Differentialligninger - 1. Graf
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1. Vektorer og matricer V Matricer
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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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VI. Egenvektorer og diagonalisering
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IX. Opgaver - 5. Januar 2005 600 Gr
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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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etningsafledede, 89, 102 retningsfe
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