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Консультация № 185328
31.01.2012, 15:39
63.05 руб.
0
6
1
Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Прошу очень подробного описания, чтобы мне понять суть
Найти точки экстремумов функции f(x,y) = ax+by при условии x2 + y2 = c2, если a=-2, b = 1, c = 1.
Прошу очень подробного описания, чтобы мне понять суть
Найти точки экстремумов функции f(x,y) = ax+by при условии x2 + y2 = c2, если a=-2, b = 1, c = 1.
Обсуждение
31.01.2012, 16:54
общий
это ответ
Здравствуйте, Посетитель - 356695!
Рассмотрим задачу: "Найти точки экстремумов функции
при условии 
"
Решение.
Геометрически задача сводится к отысканию наибольшего и наименьшего значений аппликат
плоскости 
для точек её пересечения с цилиндрической поверхностью
Составим функцию Лагранжа
и найдём её частные производные:
Необходимые условия существования экстремума определяются системой уравнений
решениями которой являются
Поскольку
постольку 
При 
и в точке 
функция 
имеет условный максимум, причём 
При 
и в точке 
функция имеет условный минимум, причём 
Итак. точка условного максимума
точка условного минимума 
С уважением.
Рассмотрим задачу: "Найти точки экстремумов функции
при условии "Решение.
Геометрически задача сводится к отысканию наибольшего и наименьшего значений аппликат
плоскости для точек её пересечения с цилиндрической поверхностью Составим функцию Лагранжа
и найдём её частные производные:Необходимые условия существования экстремума определяются системой уравнений
решениями которой являются
Поскольку
постольку При и в точке функция имеет условный максимум, причём При и в точке функция имеет условный минимум, причём Итак. точка условного максимума
точка условного минимума С уважением.
5
Об авторе:
Facta loquuntur.
Facta loquuntur.
Неизвестный
31.01.2012, 17:30
общий
31.01.2012, 18:13
Адресаты:
Андрей Владимирович, по условию коэффициент a равен -2, а не 2.
31.01.2012, 18:12
общий
Обратите, пожалуйста, внимание на мою ошибку. Ведь a = -2, а не a = 2. Сейчас переделаю решение.
Об авторе:
Facta loquuntur.
Facta loquuntur.
Форма ответа
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