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Консультация № 197466
21.12.2019, 04:55
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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
Найти экстремумы функции f(x) = (ln x) /(x)
Найти экстремумы функции f(x) = (ln x) /(x)
Обсуждение
26.12.2019, 02:11
общий
это ответ
Здравствуйте, xxgggi!
Необходимым (но не достаточным!) условием экстремума функции является равенство нулю её первой производной.
В данном случае
и из условия
получаем x = e - особая точка, возможно, являющаяся экстремумом. Для проверки найдём вторую производную функции:
и вычислим её значение в особой точке:
Отрицательное значение второй производной означает, что x = e - точка максимума.
Необходимым (но не достаточным!) условием экстремума функции является равенство нулю её первой производной.
В данном случае
и из условия
получаем x = e - особая точка, возможно, являющаяся экстремумом. Для проверки найдём вторую производную функции:
и вычислим её значение в особой точке:
Отрицательное значение второй производной означает, что x = e - точка максимума.
Форма ответа
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