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Консультация № 138028
27.05.2008, 10:45
0.00 руб.
0
1
1
4. Найти наибольшее и наименьшее значение функции на заданном отрезке.
y=2(x^2+3)/x^2-2x+5, [-3;3]
y=2(x^2+3)/x^2-2x+5, [-3;3]
Обсуждение
Неизвестный
27.05.2008, 21:00
общий
это ответ
Здравствуйте, Коленкоров Виктор Алексеевич!
y=2(x^2+3)/(x^2-2x+5), [-3;3]
y‘ = (4x(x^2-2x+5) - 2(x^2+3)(2x-2))/(x^2-2x+5)^2
(4x(x^2-2x+5) - 2(x^2+3)(2x-2))= 0
4x^3 - 8x^2 + 20x - 4x^3 + 4x^2 - 12x + 12 = 0
-4x^2 + 8x + 12 = 0
x^2 - 2x - 3 = 0
x = -1, x = 3
y(-1) = 8/8 = 1
y(3) = 24/8 = 3
y(-3) = 24/20
y наибольшее = 3
у наименьшее = 1
y=2(x^2+3)/(x^2-2x+5), [-3;3]
y‘ = (4x(x^2-2x+5) - 2(x^2+3)(2x-2))/(x^2-2x+5)^2
(4x(x^2-2x+5) - 2(x^2+3)(2x-2))= 0
4x^3 - 8x^2 + 20x - 4x^3 + 4x^2 - 12x + 12 = 0
-4x^2 + 8x + 12 = 0
x^2 - 2x - 3 = 0
x = -1, x = 3
y(-1) = 8/8 = 1
y(3) = 24/8 = 3
y(-3) = 24/20
y наибольшее = 3
у наименьшее = 1
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