若关于x的方程kx-lnx=0有解,则k的取值范围是 .
人气:336 ℃ 时间:2020-04-16 08:21:24
解答
答:
设f(x)=kx-lnx=0,x>0
求导得:
f'(x)=k-1/x
1)如果k0
当00,f(x)是增函数.
所以:当x=1/k>0时,f(x)取得最小值
所以:要使得f(x)=kx-lnx=0有实数解,必须保证最小值不大于0
所以:f(1/k)=1-ln(1/k)=e
所以:k
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