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Web skærmformat. - Aarhus Universitet

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I. Differentiation – 6. Maksimum/minimum 140<br />

Dobbelt partielle afledede<br />

fxx = 2<br />

xy3 fxx(1,1) = 2,fxy(1,1) = 1,fyy(1,1) = 2<br />

x3y ,fxy = 1<br />

x2y2 ,fyy = 2<br />

Andenordenstesten giver<br />

(a,b) f(a,b) fxx(a,b) D(a,b) Type<br />

(1,1) 3 2 3 minimum<br />

Altså er punktet (1,1) lokalt minimum for f på mængden x > 0,y > 0.<br />

6.47. Opgave ☞ Matematik Alfa 1, August 2002<br />

Opgave 3 - Figur

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