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Консультация № 196936
02.11.2019, 21:06
0.00 руб.
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Здравствуйте! У меня возникли сложности с таким вопросом:
p.s. я пробовал уже всё, что можно, никак не поддаётся
p.s. я пробовал уже всё, что можно, никак не поддаётся
Прикрепленные файлы:
Обсуждение
07.11.2019, 19:41
общий
это ответ
Здравствуйте, guyfrommatrix!
Рассмотрим функцию
Очевидно, что f(0) = 0. При x = 1 получаем выражение
которое по условию задачи равно нулю. Таким образом, f(0) = f(1) = 0, и так как функция f непрерывна и не равна тождественно нулю, то на интервале (0, 1) существуют по крайней мере один промежуток возрастания и один промежуток убывания функции, а следовательно, хотя бы одна точка, в которой функция меняет возрастание на убывание (точка локального максимума), либо убывание на возрастание (точка локального минимума). В этой точке производная функции
будет равна нулю, то есть
хотя бы в одной точке интервала (0, 1), что и требовалось доказать.
Рассмотрим функцию
Очевидно, что f(0) = 0. При x = 1 получаем выражение
которое по условию задачи равно нулю. Таким образом, f(0) = f(1) = 0, и так как функция f непрерывна и не равна тождественно нулю, то на интервале (0, 1) существуют по крайней мере один промежуток возрастания и один промежуток убывания функции, а следовательно, хотя бы одна точка, в которой функция меняет возрастание на убывание (точка локального максимума), либо убывание на возрастание (точка локального минимума). В этой точке производная функции
будет равна нулю, то есть
хотя бы в одной точке интервала (0, 1), что и требовалось доказать.
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