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Консультация № 194300
26.12.2018, 11:50
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Исследовать функцию на монотонность и экстремумы: y=3x^4-2x^3+5
Исследовать функцию на монотонность и экстремумы: y=3x^4-2x^3+5
Обсуждение
29.12.2018, 11:55
общий
это ответ
Здравствуйте, sasha181999_9!
Вычислим производную заданной функции:
Производная заданной функции определена и непрерывна на всей числовой прямой. Приравняв производную к нулю, установим критические точки заданной функции:
Вычислим вторую производную заданной функции и значения второй производной в критических точках:
Исходя из знаков второй производной в критических точках, делаем вывод, что заданная функция имеет, согласно второму достаточному условию экстремума, локальный минимум в точке
причём
Точка
не является точкой экстремума, что можно установить, например, решив неравенства
При этом оказывается, что заданная функция возрастает при
и убывает при 
Показанный ниже график иллюстрирует сделанные выводы.
Вычислим производную заданной функции:
Производная заданной функции определена и непрерывна на всей числовой прямой. Приравняв производную к нулю, установим критические точки заданной функции:
Вычислим вторую производную заданной функции и значения второй производной в критических точках:
Исходя из знаков второй производной в критических точках, делаем вывод, что заданная функция имеет, согласно второму достаточному условию экстремума, локальный минимум в точке
причёмТочка
не является точкой экстремума, что можно установить, например, решив неравенстваПри этом оказывается, что заданная функция возрастает при
и убывает при Показанный ниже график иллюстрирует сделанные выводы.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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