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Консультация № 137739
21.05.2008, 10:06
50.00 руб.
0
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1
Уважаемые эксперты! Помогите, пожалуйста, решить задачу.
Найти наибольшее и наименьшее значения функции на отрезке:
у=(х/√12)-cos x; [-π;π].
Найти наибольшее и наименьшее значения функции на отрезке:
у=(х/√12)-cos x; [-π;π].
Обсуждение
Неизвестный
21.05.2008, 21:39
общий
это ответ
Здравствуйте, Юсупова М.М.!
Найдём производную:
y‘ = ((х/√12)-cos(x))‘ = 1/√12+sin(x)
Чтобы найти стационарные точки, приравниваем производную к нулю:
1/√12+sin(x) = 0
x = -arcsin(1/√12)=-0,293
Итак, x=-arcsin(1/√12) - стационарная точка.
Сравниваем значения исходной функции в выбранной точке и на концах отрезка:
у(-π) = (-π/√12)-cos(-π) = (-π/√12)-(-1) = 0,093
у(-0,293) = (-0,293/√12)-cos(-0,293) = -1,042
у(π) = (π/√12)-cos(π) = (π/√12)-(-1) = 1,907
Следовательно:
min<sub>x∈[-π;π]</sub>y(x) = у(-0,293) = -1,042
max<sub>x∈[-π;π]</sub>y(x) = у(π) = 1,907
Good Luck!
Найдём производную:
y‘ = ((х/√12)-cos(x))‘ = 1/√12+sin(x)
Чтобы найти стационарные точки, приравниваем производную к нулю:
1/√12+sin(x) = 0
x = -arcsin(1/√12)=-0,293
Итак, x=-arcsin(1/√12) - стационарная точка.
Сравниваем значения исходной функции в выбранной точке и на концах отрезка:
у(-π) = (-π/√12)-cos(-π) = (-π/√12)-(-1) = 0,093
у(-0,293) = (-0,293/√12)-cos(-0,293) = -1,042
у(π) = (π/√12)-cos(π) = (π/√12)-(-1) = 1,907
Следовательно:
min<sub>x∈[-π;π]</sub>y(x) = у(-0,293) = -1,042
max<sub>x∈[-π;π]</sub>y(x) = у(π) = 1,907
Good Luck!
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