y=(1/x)^x (x>0)
取对数求导
lny=ln(1/x)^x= -xlnx
y'/y=-lnx-1
y'=-y(lnx+1)
y'=0==>-y(lnx+1)=0
==>lnx=-1
==>x=1/e
(0,1/e), y' >0
(1/e,+∞),y'