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Консультация № 201010
30.05.2021, 23:59
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Если функция f(x) =abs(x) не дифференцируема в точке x=0, то почему g(x) =(abs(x))^3 дифференцируема? Как это доказать?
Если функция f(x) =abs(x) не дифференцируема в точке x=0, то почему g(x) =(abs(x))^3 дифференцируема? Как это доказать?
Обсуждение
31.05.2021, 06:52
общий
это ответ
Здравствуйте, ovchar032!
Если функция
имеет в точке 
производную, то она имеет в этой точке правую и левую производные, которые совпадают.
Для функции
в точке 
имеем 
Левая и правая производные не совпадают, поэтому функция не дифференцируема в этой точке.
Для функции
в точке имеем 
Левая и правая производные совпадают, поэтому функция дифференцируема в этой точке.
Если функция
имеет в точке производную, то она имеет в этой точке правую и левую производные, которые совпадают.Для функции
в точке имеем Левая и правая производные не совпадают, поэтому функция не дифференцируема в этой точке.Для функции
в точке имеем Левая и правая производные совпадают, поэтому функция дифференцируема в этой точке.
5
Об авторе:
Facta loquuntur.
Facta loquuntur.
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