[x^(-1)]"=-x^(-2)f"(x)=1+2/x^2-a/x=(x^2-ax+2)/x^2定義域x>0所以x^2>0x^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<a<=2√2則x^2-ax+2恆大於等於0則f"(x)>=0增函式若a>2√2x^2-ax+2=0x=[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<x<[a+√(a^2-8)]/2定義域x>0綜上0<a<=2√2，f(x)是增函式a>2√2,則x>[a+√(a^2-8)]/2,0<[a-√(a^2-8)]/2時是增函式，[a-√(a^2-8)]/2<x<[a+√(a^2-8)]/2時是減函式a=3f"(x)=1+2/x^2-3/x=(x^2-3x+2)/x^2=0，x=1，x=2則x>2時是增函式，1<x<2是減函式所以x=2最小=2-3ln2x=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]