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Консультация № 191988
04.12.2017, 10:22
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Здравствуйте! Прошу помощи в следующем вопросе:
Задана функция z = f(x,y) 1) Исследовать данную функцию на экстремум. 2) Найти наибольшее и наименьшее значения функции в замкнутой области D, ограниченной заданными линиями. Сделать чертеж. z = 5x^ 2 – 3xy + y^2 , D: x = 0, x = 1, y = 0, y = 1.
Задана функция z = f(x,y) 1) Исследовать данную функцию на экстремум. 2) Найти наибольшее и наименьшее значения функции в замкнутой области D, ограниченной заданными линиями. Сделать чертеж. z = 5x^ 2 – 3xy + y^2 , D: x = 0, x = 1, y = 0, y = 1.
Обсуждение
04.12.2017, 13:39
общий
это ответ
Здравствуйте, z222c333b555!
1)
-стационарная точка
, 
, 
, 
, значит, - точка минимума
Ответ:
2) а) построим область
:
б) стационарная точка найдена в пункте 1
в) исследуем границы области:
1. нижняя сторона квадрата
точка уже исследована
один из концов отрезка - точка - уже исследована
Исследуем второй конец отрезка - точку
2. верхняя сторона квадрата
Исследуем концы отрезка - точки
и 
3. левая сторона квадрата
точка уже исследована
концы отрезка - точки и - уже исследованы
4. правая сторона квадрата
точка
не принадлежит области
концы отрезка - точки и - уже исследованы
г) Имеем:
значит,
,
Ответ:
,
1)
-стационарная точка , , , , значит, - точка минимумаОтвет:
2) а) построим область
:б) стационарная точка найдена в пункте 1
в) исследуем границы области
:1. нижняя сторона квадрата
точка
уже исследованаодин из концов отрезка - точка
- уже исследованаИсследуем второй конец отрезка - точку
2. верхняя сторона квадрата
Исследуем концы отрезка - точки
и 3. левая сторона квадрата
точка
уже исследованаконцы отрезка - точки
и - уже исследованы4. правая сторона квадрата
точка
не принадлежит области концы отрезка - точки
и - уже исследованыг) Имеем:
значит,
,Ответ:
,
5
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