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Консультация № 201538
23.10.2021, 16:52
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Уважаемые эксперты! Прошу вас ответить на следующий вопрос: Найти наименьшее и наибольшее значения функций: а) y=sinx на отрезке [-pi/3;pi] . б) ycosx на отрезке [pi/2;7pi/4]
Обсуждение
23.10.2021, 17:18
общий
Адресаты:
Начертите графики этих функций, посмотрите на них. Может, там и искать ничего не придётся, а сразу увидите Ответы.
Графики в студию. Мы подстрахуем Вас.
Графики в студию. Мы подстрахуем Вас.
24.10.2021, 17:27
общий
это ответ
Здравствуйте, lizzyzzz!
Рассмотрим первое задание.
Пусть дана функция y=sin(x) при -[$960$]/3[$8804$]x[$8804$][$960$]. Из школьного курса математики известно, что функция y=sin(x) монотонно возрастает от 0 до 1 при 0[$8804$]x[$8804$][$960$]/2. Поэтому и в рассматриваемом случае наибольшее значение функции равно 1. Функция монотонно убывает от 1 до 0 при [$960$]/2[$8804$]x[$8804$][$960$], принимая в правом конце отрезка, на котором она определена, значение, равное 0. Функция монотонно возрастает также при -[$960$]/3[$8804$]x[$8804$]0, принимая на левом конце отрезка, на котором она определена, значение, равное sin(-[$960$]/3)=-sin([$960$]/3)=-[$8730$]3/2[$8776$]-0,866. Это значение заданной функции является наименьшим.
График, иллюстрирующий решение задачи, показан в прикреплённом файле.
Рассмотрим первое задание.
Пусть дана функция y=sin(x) при -[$960$]/3[$8804$]x[$8804$][$960$]. Из школьного курса математики известно, что функция y=sin(x) монотонно возрастает от 0 до 1 при 0[$8804$]x[$8804$][$960$]/2. Поэтому и в рассматриваемом случае наибольшее значение функции равно 1. Функция монотонно убывает от 1 до 0 при [$960$]/2[$8804$]x[$8804$][$960$], принимая в правом конце отрезка, на котором она определена, значение, равное 0. Функция монотонно возрастает также при -[$960$]/3[$8804$]x[$8804$]0, принимая на левом конце отрезка, на котором она определена, значение, равное sin(-[$960$]/3)=-sin([$960$]/3)=-[$8730$]3/2[$8776$]-0,866. Это значение заданной функции является наименьшим.
График, иллюстрирующий решение задачи, показан в прикреплённом файле.
Прикрепленные файлы:
Об авторе:
Facta loquuntur.
Facta loquuntur.
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