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Консультация № 191589
28.10.2017, 21:56
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Здравствуйте! У меня возникли сложности с таким вопросом:
Найти наибольшее и наименьшее значение функции
z= xy-3x-2y в области D: x=0, x=4, y=0, y=4
Найти наибольшее и наименьшее значение функции
z= xy-3x-2y в области D: x=0, x=4, y=0, y=4
Обсуждение
28.10.2017, 23:45
общий
это ответ
Здравствуйте, Tata1207!
1) Построим область D:
2) Найдем стационарные точки:
-стационарная точка
3) Исследуем границы области D:
а) нижняя сторона квадрата
Исследуем концы отрезка - точки
и 
б) верхняя сторона квадрата
Исследуем концы отрезка - точки
и 
в) левая сторона квадрата
Концы отрезка - точки и уже исследованы
г) правая сторона квадрата
Концы отрезка - точки и уже исследованы
4) Имеем:
Тогда,
, 
Ответ:,
1) Построим область D:
2) Найдем стационарные точки:
-стационарная точка3) Исследуем границы области D:
а) нижняя сторона квадрата
Исследуем концы отрезка - точки
и б) верхняя сторона квадрата
Исследуем концы отрезка - точки
и в) левая сторона квадрата
Концы отрезка - точки
и уже исследованыг) правая сторона квадрата
Концы отрезка - точки
и уже исследованы4) Имеем:
Тогда,
, Ответ:
,
5
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