1f(x)＝x²-2(a+1)x+2alnx(a＞0) a=1 f(x)＝x²-4x+2lnx f(1)=-3 切线水平 y=-3
f'(x)=2x-2(a+1)+2a/x(a＞0) f'(x)=2x-4+2/x f'(1)=0
2 f'(x)=2x-2(a+1)+2a/x(a＞0) 令 f'(x)>=0得
(x-a)(x-1)>=0,a>=1,x>=a或0=e,【1,e】最大值f(1)=-2a-1a>=1,f(1)=-2a-1,f(e)=e^2-2e-(e-1)*2a=(e^2-2e)/(e-1)
1>a＞0,f(e)=e^2-2e-(e-1)*2a>0
a的取值范围 ((e^2-2e)/(e-1),无穷)