æ±f(x)=[ax²-(4a+1)x+4a+3]e^xçåè°åºé´
解ï¼f '(x)=(2ax-4a-1)e^x+[ax²-(4a+1)x+4a+3]e^x
=[ax²-(2a+1)x+2]e^x=(ax-1)(x-2)e^x=a(x-1/a)(x-2)e^x; å
¶ä¸e^>0ææç«ï¼æ
f'(x)ç
符å·åå³äºa(x-1/a)(x-2)ç符å·ï¼
â . å½ 0<aâ¦1/2æ¶, 1/aâ§2ï¼æ¤æ¶(-âï¼2]âª[1/aï¼+â)为åå¢åºé´ï¼[2ï¼1/a]为åååºé´ï¼
â¡ãå½aâ§1/2æ¶ï¼1/aâ¦2ï¼æ¤æ¶(-âï¼1/a]âª[2ï¼+â)为åå¢åºé´ï¼[1/aï¼2]为åååºé´ï¼
â¢. å½a<0æ¶ï¼(-âï¼1/a]âª[2, +â)为åååºé´ï¼[1/aï¼2]为åå¢åºé´ï¼[1/aï¼2]为åå¢åºé´ï¼
â£ãå½a=0æ¶f(x)=(-x+3)e^xï¼f '(x)=-e^x+(-x+3)e^x=(-x+2)e^x;
æ¤æ¶å½xâ§2æ¶-x+2â¦0ï¼å³f'(x)â¦0ï¼æ
å¨åºé´(-âï¼2]å
åè°åï¼å½xâ¦2æ¶-x+2â§0ï¼æ
å¨åºé´
[2ï¼+â)å
åè°å¢ã
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