11. z=2xy, x2+y2 1 doirada
12. z=x2+y2-xy+x+y. x=0, y=0, x+y=-3 to‘g‘ri chiziqlar bilan chegaralangan uchburchakda.
13. z=1-x2-y2, (x-1)2+(y-1)2 1 sohada.
Quyidagi funksiyalarning ekstremal nuqtalarini toping:
14. z=xy2(1-x-y)
15. ![](data:image/png;base64,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)
16.
17. z=x3+y3-15xy
18.
Funksiyalarning ko‘rsatilgan sohalardagi eng katta va eng kichik qiymatlarini toping:
19. z=x2+2xy-4x+8y, x=0, y=0, x=1, y=2 to‘g‘ri chiziqlar bilan chegaralangan to‘rtburchakda
20. z=arctg(x2-xy+y), x=-2, x=2, y=-3, y=3 to‘g‘ri chiziqlar bilan chegaralangan to‘rtburchaklarda.
21. Quyidagi funksiyalarning shartli ekstremumlarini toping:
a) z = xy, x + y = 1.
b) z = + , x + y = 2
c) z = x + 2y, x2 +y2 = 5
d) z = x2 + y2, + = 1
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