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Консультация № 194301
26.12.2018, 11:51
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Здравствуйте! Прошу помощи в следующем вопросе:
Исследовать функцию на промежутки выпуклости/вогнутости и точки перегиба: y=ln(x^2+1)
Исследовать функцию на промежутки выпуклости/вогнутости и точки перегиба: y=ln(x^2+1)
Обсуждение
29.12.2018, 12:04
общий
это ответ
Здравствуйте, sasha181999_9!
Дважды продифференцируем заданную функцию:
Поскольку
при всех значениях 
постольку знаки второй производной совпадают со знаками и нулями выражения 
Это выражение равно нулю при 
оно положительное при 
и отрицательное при 
Значит, график заданной функции направлен выпуклостью вниз при и выпуклостью вверх при Точки 
-- точки перегиба графика функции.
Показанный ниже график иллюстрирует сделанный вывод.
Дважды продифференцируем заданную функцию:
Поскольку
при всех значениях постольку знаки второй производной совпадают со знаками и нулями выражения Это выражение равно нулю при оно положительное при и отрицательное при Значит, график заданной функции направлен выпуклостью вниз при и выпуклостью вверх при Точки -- точки перегиба графика функции.Показанный ниже график иллюстрирует сделанный вывод.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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