ä½å½æ°y=(lnx)/xçå¾å½¢ï¼æ±è¿ç¨
解ï¼å®ä¹åï¼x>0ï¼xâ0limy=-âï¼xâ+âlim[(lnx)/x]=xâ+âlim(1/x)=0ï¼
令y'=(1-lnx)/x²=0ï¼å¾1-lnx=0ï¼lnx=1ï¼æ å¾é©»ç¹x=eï¼x<eæ¶y'>0ï¼x>eæ¶y'<0ï¼æ x=e
æ¯æ大ç¹ï¼æ大å¼y=y(e)=1/eï¼å¦å¤ï¼å½x=1æ¶y=0ï¼å³æé¶ç¹(1ï¼0)ï¼
令y''=[x²(-1/x)-(1-lnx)•2x]/x^4=(-3x+2xlnx)/x^4=(-3+2lnx)/x³=0 ï¼
å¾ x=e^(3/2)â4.5,å³å¾æç¹(e^(3/2)ï¼3/2e^(3/2))â(4.5ï¼1/3)ï¼
x<e^(3/2)æ¶y''<0ï¼x>e^(3/2)æ¶y''>0ï¼æ (0ï¼e^(3/2]为å¸åºé´ï¼[e^(3/2),+âï¼
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