f(x)=√(x^2+1)-ax(a>0)
显然,定义域为实数范围R
求导:
f'(x)=2x/[2√(x^2+1)]-a
=x/√(x^2+1)-a
f(x)在x>=1时是单调递增函数
所以:f'(x)=x/√(x^2+1)-a>=0在x>=1时恒成立
a<=x/√(x^2+1)
=√[x^2/(x^2+1)]
=√[1-1/(x^2+1)]
x>=1,x^2+1>=2
-1/2<=-1/(x^2+1)<0
1/2<=1-1/(x^2+1)<1
所以:a<=√(1/2)<=√[1-1/(x^2+1)]
所以:0
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