f'(x)=1+2/x^2-a/x=(x^2-ax+2)/x^2
定義域x>0
所以x^2>0
x^2-ax+2=(x-a/2)^2-a^2/4+2
若2-a^2/4>=0
-2√2<=a<=2√2,又a>0
即0
則f'(x)>=0
增函數(shù)
若a>2√2
x^2-ax+2=0
x=[a±√(a^2-8)]/2
則若x^2-ax+2>0,x>[a+√(a^2-8)]/2,x<[a-√(a^2-8)]/2
若x^2-ax+2<0,[a-√(a^2-8)]/2
綜上
0
[a-√(a^2-8)]/2
f'(x)=1+2/x^2-3/x=(x^2-3x+2)/x^2=0,x=1,x=2
則x>2時(shí)是增函數(shù),
1
x=1或e^2最大
f(e^2)=e^2-2/e^2-5最大
[2-3ln2,e^2-2/e^2-5]