函数y=(x的四次方+x²+5)/(x²+1)²的最大值与最小值的和为
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函数y=(x的四次方+x²+5)/(x²+1)²的最大值与最小值的和为
函数y=(x的四次方+x²+5)/(x²+1)²的最大值与最小值的和为
函数y=(x的四次方+x²+5)/(x²+1)²的最大值与最小值的和为
对函数求导,令为0,求驻点为
x=0,-3,3
对应的函数值y=5,0.95,0.95
所以答案是5.95
解法如下:
y=(x^4+x^2+5)/(x^2+1)^2
={(x^2+1)^2-(x^2+1)+5}/(x^2+1)^2
=1-1/(x^2+1)+5/(x^2+1)^2
y'=-38x/(x^2+1)^2
解得:x=0
由此可确定y(x)函数性质
y(x)max=y(0)=5
y(x)min=1
sum=min+max=6.