f(x)=lnx-1/xçå®ä¹å为x>0
f(x)å¨å®ä¹åå
æ¯å¢å½æ°.
设0f(x1)-f(x2)=lnx1-1/x1-(lnx2-1/x2)
=lnx1-lnx2+1/x2-1/x1
=ln(x1/x2)+(x1-x2)/(x1x2)
âµ0â´x1/x2<1
ln(x1/x2)<0
x1-x2<0
x1x2>0
â´(x1-x2)/(x1x2)<0
ln(x1/x2)+(x1-x2)/(x1x2)<0
å³ï¼f(x1)-f(x2)<0
f(x1)å½æ°f(x)为å¢å½æ°.
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