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Консультация № 194483
20.01.2019, 18:56
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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
При каком условии кубическая парабола y = x^3 + px + q касается оси Ox?
Тут я не совсем понимаю, что от меня хотят. Найти связь между p и q?
При каком условии кубическая парабола y = x^3 + px + q касается оси Ox?
Тут я не совсем понимаю, что от меня хотят. Найти связь между p и q?
Обсуждение
24.01.2019, 06:32
общий
это ответ
Здравствуйте, ms.any2000!
Если график функции касается оси
то в точках касания производная функции равна нулю. Значит,
а абсциссы точек касания графика функции с осью
суть
При этом
С другой стороны при установленных выше значениях
и 
имеем 
Тогда
Следовательно, если
то
Если же
то
Ответ: должно выполняться условие (1) и одно из условий (2), (3).
Если график функции касается оси
то в точках касания производная функции равна нулю. Значит,а абсциссы точек касания графика функции с осью
сутьПри этом
С другой стороны при установленных выше значениях
и имеем ТогдаСледовательно, если
тоЕсли же
тоОтвет: должно выполняться условие (1) и одно из условий (2), (3).
Об авторе:
Facta loquuntur.
Facta loquuntur.
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