试题与答案

已知函数f(x)=mx-m-1x-lnx(m∈R),g(x)=1x+lnx.(I

题型:解答题

题目:

已知函数f(x)=mx-
m-1
x
-lnx(m∈R),g(x)=
1
x
+lnx

(I)求g(x)的极小值;
(II)若y=f(x)-g(x)在[1,+∞)上为单调增函数,求m的取值范围;
(III)设h(x)=
2e
x
,若在[1,e]
(e是自然对数的底数)上至少存在一个x0,使得f(x0)-g(x0)>h(x0)成立,求m的取值范围.

答案:

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