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Консультация № 188223
23.11.2015, 00:04
0.00 руб.
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1
Здравствуйте! У меня возникли сложности с таким вопросом:
Найти все значения a, при которых неравенство f'(x)<0 не имеет действительных решений, если f(x)=(((a-4)/3)*x^3+x^2-x-4)
Найти все значения a, при которых неравенство f'(x)<0 не имеет действительных решений, если f(x)=(((a-4)/3)*x^3+x^2-x-4)
Обсуждение
24.11.2015, 06:46
общий
Адресаты:
Воспользуйтесь формулой (cx^n)'=cnx^(n-1).
Об авторе:
Facta loquuntur.
Facta loquuntur.
25.11.2015, 10:14
общий
это ответ
Здравствуйте, Посетитель - 399097!
Имеем
Выражение (1) задаёт квадратичную функцию, графиком которой является парабола. При
ветви параболы направлены вверх, а при 
- вниз.
Воспользуемся тем, что график квадратного трёхчлена не пересекает ось абсцисс, если дискриминант квадратного уравнения
отрицателен. Тогда
Но при
получаем 
т. е. ветви параболы направлены вниз. Поэтому неравенство 
будет иметь действительные решения. Значит, задача не имеет решения, как я понимаю.
С уважением.
Имеем
Выражение (1) задаёт квадратичную функцию, графиком которой является парабола. При
ветви параболы направлены вверх, а при - вниз.Воспользуемся тем, что график квадратного трёхчлена не пересекает ось абсцисс, если дискриминант квадратного уравнения
отрицателен. ТогдаНо при
получаем т. е. ветви параболы направлены вниз. Поэтому неравенство будет иметь действительные решения. Значит, задача не имеет решения, как я понимаю.С уважением.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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