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已知函数f(x)=lnx/x+1/x.

已知函数f(x)=lnx/x+1/x.
当x>=1时,不等式f(x)>=k/(x+1)恒成立,求实数K的取值范围.
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f(x)>=k/(x+1)变形得f(x)(x+1)>=k 得:(x+1)(lnx/x+1/x)=lnx+1+lnx/x+1/x 设为:g(x) 求导:得 1/x+(1-lnx)/x²-1/x²=(x-lnx)/x² 将分子设为h(x)因为分母大于0恒成立,所以讨论分子的正负性 求导得:1-1/x ∵x>=1∴1-1/x 大于0恒成立 ∴h(x)为单增函数,最小值为h(1)=1∴g...

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