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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос: Найти наибольшее и наименьшее значения функции z=f(x,y) в замкнутой области D. Сделать рисунок области D. z=2x^2+2xy-(1/2)y^2-4x ; D: x=0, y=2, y=2x.
По сути дела Вы попросили не ответить на вопрос, а выполнить вместо Вас выданное Вам задание. Я мог бы выполнить его сам примерно за один час, но мне хочется, чтобы Вы тоже поучаствовали в этом. Поэтому я предлагаю Вам следующее: Цитата: sirkrutfm
Область показана в прикреплённом файле заливкой серым цветом. Масштабы по осям разные.
Определим стационарные точки функции
Следовательно, -- единственная стационарная точка функции Она принадлежит границе области (участку ). Значение функции в этой точке
На участке Экстремум достигается в точке (смотрите выше). На концах отрезка
На участке при то есть в точке
На участке при то есть в точке
Сопоставляя полученные результаты, приходим к выводу, что наименьшее значение функции достигается в точке и равно Наибольшее значение функции достигается в точках и равно
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sirkrutfm 
показана в прикреплённом файле заливкой серым цветом. Масштабы по осям разные.
-- единственная стационарная точка функции 
Она принадлежит границе области 
). Значение функции в этой точке 
Экстремум достигается в точке 
(смотрите выше). На концах отрезка 
при 
то есть в точке 
при 
то есть в точке 
и равно 
Наибольшее значение функции достигается в точках 
и равно 
