f(x)=x的平方+2x+3除以x的平方+1最大值及最小值?
回答 (1)
2017-09-20 7:11 pm
f(x)=(x^2+2x+3)/(x^2+1)最大值及最小值?
Sol
p=(x^2+2x+3)/(x^2+1)
x^2+2x+3=px^2+p
(p－1)x^2－-2x+(p－3)=0
D=(－2)^2－4*(p－1)(p－3)>=0
1－(p－1)(p－3)>=0
1－(p^2－4p+3)>=0
－p^2+4p－2>=0
p^2－4p+2<=0
p^2－4p<=-2
p^2－4p+4<=2
(p－2)^2-2<=0
(p－2－√2)(p－2+√2)<=0
2－√2<=p<=2+√2
Sol
p=(x^2+2x+3)/(x^2+1)
x^2+2x+3=px^2+p
(p－1)x^2－-2x+(p－3)=0
D=(－2)^2－4*(p－1)(p－3)>=0
1－(p－1)(p－3)>=0
1－(p^2－4p+3)>=0
－p^2+4p－2>=0
p^2－4p+2<=0
p^2－4p<=-2
p^2－4p+4<=2
(p－2)^2-2<=0
(p－2－√2)(p－2+√2)<=0
2－√2<=p<=2+√2
收錄日期: 2021-04-30 22:10:10
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20170920103559AADHBqj