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Консультация № 201347
16.08.2021, 10:48
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Здравствуйте! У меня вопрос возник при определении наибольшем и наименьшем значении функции. Пример f(x)=x^3-3x^2+12x-10 на отрезке от [0 до 10], тут же производная всегда >0, т.е. тут нельзя найти наиб. и наим значение?
Обсуждение
16.08.2021, 10:58
общий
Адресаты:
"производная всегда >0" означает отсутствие Максимума (с перегибом).
В таких случаях наибольшее и наименьшее значения функции ищут на краях заданного аргумент-отрезка.
В таких случаях наибольшее и наименьшее значения функции ищут на краях заданного аргумент-отрезка.
16.08.2021, 11:02
общий
это ответ
Если бы на всей числовой прямой, то да, нельзя.
А нам задан отрезок.
Если производная функции положительна на всем отрезке, то значит, на этом отрезке функция монотонно возрастает, тогда наименьшее значение в левом конце отрезка, то есть при
, а наибольшее в правом конце отрезка, то есть при 
. Да и даже, если не выяснять положительна производная или отрицательна, концы отрезка нужно исследовать всегда.
нет корней
значит,
наиб
, 
наим
Ответ:наиб
, наим
А нам задан отрезок.
Если производная функции положительна на всем отрезке, то значит, на этом отрезке функция монотонно возрастает, тогда наименьшее значение в левом конце отрезка, то есть при
, а наибольшее в правом конце отрезка, то есть при . Да и даже, если не выяснять положительна производная или отрицательна, концы отрезка нужно исследовать всегда.нет корней
значит,
наиб, наимОтвет:
наиб, наим
16.08.2021, 13:35
общий
Адресаты:
НаЗдоровье Вам!
Михаил Александров отправил Вам Ответ. Вы видели его?
Михаил Александров отправил Вам Ответ. Вы видели его?
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