已知函数f(x)=lnx-ax.(a∈R)(Ⅰ)求函数f(x)的单调增区间;(Ⅱ)若a=-2,求函数f(x)在[1,e]

2024-10-31 23:18:24
推荐回答(1个)
回答(1):

(I)∵f′(x)=

x+a
x2

①a≥0时,f′(x)>0,f(x)在(0,+∞)递增,
②a<0时,令f′(x)>0,解得:x>-a,
∴f(x)在(-a,+∞)递增,
(Ⅱ)a=-
2
时,f′(x)=
x?
2
x2

f(x)在(1,
2
)递减,在(
2
,e)递增,
∴f(x)min=f(
2
)=ln(
2
)+1=
1
2
ln2+1.