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求函数y=(x^4+x^2+5)/(x^2+1)^2的最大值与最小值

学习时间:2026-08-14 05:40:00 阅读：3781

求函数y=(x^4+x^2+5)/(x^2+1)^2的最大值与最小值

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2026-08-14 05:40:00

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y=(x^4+x^2+5)/(x^4+2x^2+1) =(x^4+2x^2+1-x^2+4)/(x^4+2x^2+1) =1+(4-x^2)/(x^4+2x^2+1) =1+(5-(x^2+1))/(x^2+1)^2 =1-1/(x^2+1)+5/(x^2+1)^2令t=1/(x^2+1) ,0

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2026-08-14 05:40:00
y=(x^4+x^2+5)/(x^4+2x^2+1) =(x^4+2x^2+1-x^2+4)/(x^4+2x^2+1) =1+(4-x^2)/(x^4+2x^2+1) =1+(5-(x^2+1))/(x^2+1)^2 =1-1/(x^2+1)+5/(x^2+1)^2令t=1/(x^2+1) ,0

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