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Mathematics 1
Mathematics 1 Deneme Sınavı
Mathematics 1 Deneme Sınavı Sorusu #1264617
Mathematics 1 Deneme Sınavı Sorusu #1264617
Which of the following is the local minimum point of the function f(x,y)=2x²+2xy+2y²-6x ?
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(2,-1) |
|
(2,-2) |
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(-2,-1) |
|
(-2,0) |
|
(0,2) |
Yanıt Açıklaması:
?f / ?x = 4x+ 2y-6 ?f / ?y=2x+4y
for the critical points;
4x+ 2y-6=0 and 2x+4y=0, so x=2, y=-1.
?²f / ?x² =4 ?²f / ?y² =4 ?f / ?xy =2
D=4.4-2²=12.
Since D>0, the function has a local minimum at (2,-1).
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