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Консультация № 196448
24.09.2019, 16:33
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Здравствуйте! У меня возникли сложности с таким вопросом:
найти наибольшее и наименьшее значение функции z=f(x,y) в замкнутой области : z=2(x)^2-4xy+5(y)^2-8x+6, где x[$8805$]2 , y[$8805$]0 , x+y[$8805$]5. помогите пожалуйста!!!
найти наибольшее и наименьшее значение функции z=f(x,y) в замкнутой области : z=2(x)^2-4xy+5(y)^2-8x+6, где x[$8805$]2 , y[$8805$]0 , x+y[$8805$]5. помогите пожалуйста!!!
Обсуждение
26.09.2019, 16:00
общий
это ответ
Здравствуйте, oksana.nevalenaya!
Заданная замкнутая область показана на рисунке в прикреплённом файле. Она представляет собой часть плоскости, ограниченную треугольником с вершинами в точках
Для решения задачи воспользуемся методикой [1, с. 277 -- 278].
Здесь
1. Установим все критические точки.
Решением системы является точка
Она принадлежит заданной замкнутой области. Значение функции в этой точке 
2. Исследуем функцию
на границе области, состоящей из участков 
На участке
имеем 
где 
Значения функции 
На участке
имеем 
где 
Значения функции 
На участке
имеем 
где 
Значения функции 
3. Сравнивая полученные результаты, имеем
-- наибольшее значение функции, 
-- наименьшее значение функции.
Литература
1. Письменный Д. Т. Конспект лекций по высшей математике. В. 2 ч. Ч. 1. -- М.: Айрис-пресс, 2006. -- 288 с.
Обязательно проверьте мой расчёт во избежание ошибок!
Заданная замкнутая область показана на рисунке в прикреплённом файле. Она представляет собой часть плоскости, ограниченную треугольником с вершинами в точках
Для решения задачи воспользуемся методикой [1, с. 277 -- 278].
Здесь
1. Установим все критические точки.
Решением системы является точка
Она принадлежит заданной замкнутой области. Значение функции в этой точке 2. Исследуем функцию
на границе области, состоящей из участков На участке
имеем где Значения функции На участке
имеем где Значения функции На участке
имеем где Значения функции 3. Сравнивая полученные результаты, имеем
-- наибольшее значение функции, -- наименьшее значение функции.Литература
1. Письменный Д. Т. Конспект лекций по высшей математике. В. 2 ч. Ч. 1. -- М.: Айрис-пресс, 2006. -- 288 с.
Обязательно проверьте мой расчёт во избежание ошибок!
Прикрепленные файлы:
5
Об авторе:
Facta loquuntur.
Facta loquuntur.
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