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Консультация № 132481
16.04.2008, 19:27
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Уважаемые эксперты, помогите справиться с заданием:
Решите неравенство:
f´(x)>=f´´(x), если f(x)=(2х-1)^6
Нужно как можно быстрее...заранее огромное спасибо...
Решите неравенство:
f´(x)>=f´´(x), если f(x)=(2х-1)^6
Нужно как можно быстрее...заранее огромное спасибо...
Обсуждение
Неизвестный
16.04.2008, 19:49
общий
это ответ
Здравствуйте, Attalea!
Найдем первую и вторую производные этой функции по правилу производной степенной функции.
f‘(x)=6(2x-1)^5
f‘‘(x)=30(2x-1)^4
Приходим к неравенству
6(2х-1)^5>=30(2х-1)^4 или равносильное
(2х-1)^5>=5(2х-1)^4
При х=1/2 0>=0 - неравенство выполняется. Для х не равных 1/2 поделим обе части неравенства на (2х-1)^4. Четвертая степень любого числа-число положительное, поэтому знак неравенства не изменится.
2х-1>=5
х>=3.
Ответ: х?{1/2}U[3; +беск.).
Найдем первую и вторую производные этой функции по правилу производной степенной функции.
f‘(x)=6(2x-1)^5
f‘‘(x)=30(2x-1)^4
Приходим к неравенству
6(2х-1)^5>=30(2х-1)^4 или равносильное
(2х-1)^5>=5(2х-1)^4
При х=1/2 0>=0 - неравенство выполняется. Для х не равных 1/2 поделим обе части неравенства на (2х-1)^4. Четвертая степень любого числа-число положительное, поэтому знак неравенства не изменится.
2х-1>=5
х>=3.
Ответ: х?{1/2}U[3; +беск.).
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