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14、
f(x)=(x^2+1)/(4x)
f'(x)=[2x×4x-(x^2+1)×4]/(4x)^2
=(8x^2-4x^2-4)/(4x)^2
=(x^2-1)/(4x^2)
=(x+1)(x-1)/(4x^2)
减函数:f'(x)<=0
(x+1)(x-1)/(4x^2)<=0
(x+1)(x-1)<=0
-1=<x<=1
f(x)在(0,2m-1)上单调递减
0<2m-1<=1
1<2m<=2
1/2<m<=1
m的取值范围:(1/2,1]
f(x)=(x^2+1)/(4x)
f'(x)=[2x×4x-(x^2+1)×4]/(4x)^2
=(8x^2-4x^2-4)/(4x)^2
=(x^2-1)/(4x^2)
=(x+1)(x-1)/(4x^2)
减函数:f'(x)<=0
(x+1)(x-1)/(4x^2)<=0
(x+1)(x-1)<=0
-1=<x<=1
f(x)在(0,2m-1)上单调递减
0<2m-1<=1
1<2m<=2
1/2<m<=1
m的取值范围:(1/2,1]
追问
f(x)是怎么变成f'(x)的
追答
f'(x)是f(x)的导函数,就是f(x)对x求导即可得到f'(x)
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