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Консультация № 139341
06.06.2008, 17:00
0.00 руб.
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2
2
Здравствуйте эксперты. Найти наибольшее и наименьшее значения функции на отрезке.
f(x)=x+8-4*(кореньx+2); [-1;7]
f(x)=x+8-4*(кореньx+2); [-1;7]
Обсуждение
Неизвестный
06.06.2008, 20:24
общий
это ответ
Здравствуйте, SETXAOS!
f(x)=x+8-4*(кореньx+2); [-1;7]
f‘ = 1-2/√(x+2)
√(x+2) - 2 = 0
√(x+2) = 2
x + 2 = 4
x = 2
f(-1) = -1 + 8 -4*√1 = 3
f(2) = 2 + 8 - 4*√4 = 2
f(7) = 7 + 8 -4*√9 = 3
Ответ: наим знач 2, наиб знач 3
f(x)=x+8-4*(кореньx+2); [-1;7]
f‘ = 1-2/√(x+2)
√(x+2) - 2 = 0
√(x+2) = 2
x + 2 = 4
x = 2
f(-1) = -1 + 8 -4*√1 = 3
f(2) = 2 + 8 - 4*√4 = 2
f(7) = 7 + 8 -4*√9 = 3
Ответ: наим знач 2, наиб знач 3
08.06.2008, 12:10
общий
это ответ
Здравствуйте, SETXAOS!
Решение.
Находим производную функции:
f‘(x) = 1 - 4*(1/(2*sqrt (x + 2))) = 1 - 2/sqrt (x + 2).
Находим точки, в которых производная обращается в нуль:
1 - 2/sqrt (x + 2) = 0,
2/sqrt (x + 2) = 1,
sqrt (x + 2) = 2,
x + 2 = 4,
x = 2.
Полученная точка принадлежит отрезку [-1; 7]. Находим значение функции в этой точке:
f(2) = 2 + 8 - 4*sqrt (2 + 2) = 2 + 8 - 8 = 2.
Находим значения функции на концах отрезка:
f(-1) = -1 + 8 - 4*sqrt (-1 + 2) = -1 + 8 - 4 = 3,
f(7) = 7 + 8 - 4*sqrt (7 + 2) = 7 + 8 - 12 = 3.
Следовательно, f наиб. = 3, f наим. = 2.
Ответ: f наиб. = 3, f наим. = 2.
С уважением.
Решение.
Находим производную функции:
f‘(x) = 1 - 4*(1/(2*sqrt (x + 2))) = 1 - 2/sqrt (x + 2).
Находим точки, в которых производная обращается в нуль:
1 - 2/sqrt (x + 2) = 0,
2/sqrt (x + 2) = 1,
sqrt (x + 2) = 2,
x + 2 = 4,
x = 2.
Полученная точка принадлежит отрезку [-1; 7]. Находим значение функции в этой точке:
f(2) = 2 + 8 - 4*sqrt (2 + 2) = 2 + 8 - 8 = 2.
Находим значения функции на концах отрезка:
f(-1) = -1 + 8 - 4*sqrt (-1 + 2) = -1 + 8 - 4 = 3,
f(7) = 7 + 8 - 4*sqrt (7 + 2) = 7 + 8 - 12 = 3.
Следовательно, f наиб. = 3, f наим. = 2.
Ответ: f наиб. = 3, f наим. = 2.
С уважением.
Об авторе:
Facta loquuntur.
Facta loquuntur.
Форма ответа
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