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Консультация № 199799
07.12.2020, 01:48
0.00 руб.
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Здравствуйте! Прошу помощи в следующем вопросе:
Исследовать на выпуклость, вогнутость и найти точки перегиба функции.
Исследовать на выпуклость, вогнутость и найти точки перегиба функции.
Прикрепленные файлы:
Обсуждение
13.12.2020, 18:58
общий
это ответ
Здравствуйте, svrvsvrv!
Найдём первую и вторую производные функции:
и определим их значения (с точностью до знака):
(стрелками обозначены интервалы возрастания/убывания функции, знаки [$8745$]/[$8746$]/[$967$] указывают на выпуклость/вогнутость/перегиб). Таким образом, функция выпукла при |x| > 1 (y" < 0), вогнута при |x| < 1 (y" > 0) и имеет две точки перегиба при x = [$177$]1.
Найдём первую и вторую производные функции:
и определим их значения (с точностью до знака):
(стрелками обозначены интервалы возрастания/убывания функции, знаки [$8745$]/[$8746$]/[$967$] указывают на выпуклость/вогнутость/перегиб). Таким образом, функция выпукла при |x| > 1 (y" < 0), вогнута при |x| < 1 (y" > 0) и имеет две точки перегиба при x = [$177$]1.
5
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