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Консультация № 200789
05.05.2021, 11:04
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Здравствуйте! У меня возникли сложности с таким вопросом:
Найти наибольшее и наименьшее значение фугкции z=z(x;y) в замкнутой области D,ограниченной заданнами линиями. z=3x^2+3y^2-x-y+1, D : x=5,y=0,x-y-1=0
Найти наибольшее и наименьшее значение фугкции z=z(x;y) в замкнутой области D,ограниченной заданнами линиями. z=3x^2+3y^2-x-y+1, D : x=5,y=0,x-y-1=0
Обсуждение
05.05.2021, 15:33
общий
это ответ
Здравствуйте, tatevvardanyan9476!
Область
показана на рисунке в прикреплённом файле окрашенной в серый цвет.
Имеем
Определим критические точки:
Решением системы является точка
которая не принадлежит области 
Исследуем функцию
на границе области, состоящей из участков 
На участке
-- точки с этой абсциссой не принадлежат области Значения функции на концах отрезка 
На участке
точки с этой абсциссой не принадлежат области Значения функции на концах отрезка 
На участке
Значения функции на концах отрезка 
Сравнивая полученные результаты, имеем
Литература
Письменный Д. Т. Конспект лекций по высшей математике: [в 2 ч.]. Ч. 1. -- М.: Айрис-пресс, 2007.
Если Вы хотите воспользоваться этим решением задачи, то, пожалуйста, проверьте его во избежание ошибок.
Область
показана на рисунке в прикреплённом файле окрашенной в серый цвет.Имеем
Определим критические точки:
Решением системы является точка
которая не принадлежит области Исследуем функцию
на границе области, состоящей из участков На участке
-- точки с этой абсциссой не принадлежат области Значения функции на концах отрезка На участке
точки с этой абсциссой не принадлежат области Значения функции на концах отрезка На участке
Значения функции на концах отрезка Сравнивая полученные результаты, имеем
Литература
Письменный Д. Т. Конспект лекций по высшей математике: [в 2 ч.]. Ч. 1. -- М.: Айрис-пресс, 2007.
Если Вы хотите воспользоваться этим решением задачи, то, пожалуйста, проверьте его во избежание ошибок.
Прикрепленные файлы:
Об авторе:
Facta loquuntur.
Facta loquuntur.
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