f(x)=x-alnx
å®ä¹åx>0
f'(x)=1-a/x
a<0 f'(x)>0 f(x)åè°éå¢ lim(xâ0)f(x)=-â,ä¸çå¼æ æ³ææç«
a>0
é©»ç¹x=1/a
0<x<1/a f'(x)<0 f(x)åè°éå,x>1/a f'(x)>0 f(x)åè°éå¢
â´f(1/a)=1/a+alnaæ¯æå°å¼
å½f(1/a)â¥aæ¶ä¸çå¼ææç«
令g(a)=1/a+alna-a
g'(a)=-1/a²+lna
é©»ç¹ï¼a₁²lna₁=1 a₁â1.53 g(a₁)<0,
â´g(a)æ两个é¶ç¹a₁=1ï¼a₂â2.21845749ã
â´0<a<a₁ g(a)åè°éå¢ a>a₂ g(a)åè°éå¢
â´açåå¼èå´0<aâ¤1âªaâ¥a₂
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