已知函数f(x)=x-x分之a+2分之a在区间(1,+∞)是增函数,求实数a的取值范围.如题

Question

已知函数f(x)=x-x分之a+2分之a在区间(1,+∞)是增函数,求实数a的取值范围.
如题

Answer 1

设x1,x2∈(1,+∞),且x1＜x2
f(x1)-f(x2)
=x1-a/x1+a/2-x2+a/x2-a/2
=x1-a/x1-x2+a/x2
=(x1-x2)-a(1/x1-1/x2)
=(x1-x2)-a(x2-x1)/x1x2
=(x1-x2)+a(x1-x2)/x1x2
=(x1-x2)(x1x2+a)/x1x2＜0
a＞-1