µÚ3½² µ¼ÊýÓ뺯ÊýµÄ¼«Öµ¡¢×îÖµ
1£®º¯Êýy£½xÔÚ[0£¬2]ÉϵÄ×î´óÖµÊÇ( )
e1
A£® eC£®0
2B£®2 e1D£® 2e
x1£x½âÎö£ºÑ¡A£®Ò×Öªy¡ä£½x£¬x¡Ê[0£¬2]£¬Áîy¡ä>0£¬µÃ0¡Üx<1£¬Áîy¡ä<0£¬µÃ2¡Ýx>1£¬
eËùÒÔº¯Êýy£½xÔÚ[0£¬1]Éϵ¥µ÷µÝÔö£¬ÔÚ(1£¬2]Éϵ¥µ÷µÝ¼õ£¬ËùÒÔy£½xÔÚ[0£¬2]ÉϵÄ×î´óÖµ
ee1
ÊÇy|x£½1£½£¬¹ÊÑ¡A£®
e
2£®ÒÑÖªaΪº¯Êýf(x)£½x£12xµÄ¼«Ð¡Öµµã£¬Ôòa£½( ) A£®£4 C£®4
2
3
xxB£®£2 D£®2
½âÎö£ºÑ¡D.ÓÉÌâÒâµÃf¡ä(x)£½3x£12£¬ÓÉf¡ä(x)£½0µÃx£½¡À2£¬µ±x¡Ê(£¡Þ£¬£2)ʱ£¬f¡ä(x)>0£¬º¯Êýf(x)µ¥µ÷µÝÔö£¬µ±x¡Ê(£2£¬2)ʱ£¬f¡ä(x)<0£¬º¯Êýf(x)µ¥µ÷µÝ¼õ£¬µ±x¡Ê(2£¬£«¡Þ)ʱ£¬f¡ä(x)>0£¬º¯Êýf(x)µ¥µ÷µÝÔö£¬ËùÒÔa£½2.
3£®º¯Êýf(x)£½x£«bx£«cx£«dµÄ´óÖÂͼÏóÈçͼËùʾ£¬Ôòx1£«x2µÈÓÚ( )
3
2
2
2
8A£® 916C£® 9
10B£®
928D£®
9
½âÎö£ºÑ¡C£®º¯Êýf(x)µÄͼÏó¹ýԵ㣬ËùÒÔd£½0.ÓÖf(£1)£½0ÇÒf(2)£½0£¬¼´£1£«b£c£½0ÇÒ8£«4b£«2c£½0£¬½âµÃb£½£1£¬c£½£2£¬ËùÒÔº¯Êýf(x)£½x£x£2x£¬ËùÒÔf¡ä(x)£½3x£2x£2£¬ÓÉÌâÒâÖªx1£¬x2ÊǺ¯ÊýµÄ¼«Öµµã£¬ËùÒÔx1£¬x2ÊÇf¡ä(x)£½0µÄÁ½¸ö¸ù£¬ËùÒÔ
22
x1£«x2£½£¬x1x2£½££¬ËùÒÔx2. 1£«x2£½(x1£«x2)£2x1x2£½£«£½2
3
2
2
3234416939
4£®ÒÑÖªº¯Êýf(x)£½x£«3x£9x£«1£¬Èôf(x)ÔÚÇø¼ä[k£¬2]ÉϵÄ×î´óֵΪ28£¬ÔòʵÊýkµÄÈ¡Öµ·¶Î§Îª( )
32
1
A£®[£3£¬£«¡Þ) C£®(£¡Þ£¬£3)
2
B£®(£3£¬£«¡Þ) D£®(£¡Þ£¬£3]
½âÎö£ºÑ¡D.ÓÉÌâÒâÖªf¡ä(x)£½3x£«6x£9£¬Áîf¡ä(x)£½0£¬½âµÃx£½1»òx£½£3£¬ËùÒÔ
f¡ä(x)£¬f(x)ËæxµÄ±ä»¯Çé¿öÈçÏÂ±í£º
x f¡ä(x) f(x) (£¡Þ£¬£3) £« £3 0 ¼«´óÖµ (£3£¬1) £ 1 0 ¼«Ð¡Öµ (1£¬£«¡Þ) £« ÓÖf(£3)£½28£¬f(1)£½£4£¬f(2)£½3£¬f(x)ÔÚÇø¼ä[k£¬2]ÉϵÄ×î´óֵΪ28£¬ËùÒÔk¡Ü£3.
5£®Èôº¯Êýf(x)£½x£3axÔÚÇø¼ä(£1£¬2)ÉϽöÓÐÒ»¸ö¼«Öµµã£¬ÔòʵÊýaµÄÈ¡Öµ·¶Î§Îª( )
A£®(1£¬4] C£®[1£¬4)
2
3
B£®[2£¬4] D£®[1£¬2]
½âÎö£ºÑ¡C£®ÒòΪf¡ä(x)£½3(x£a)£¬ËùÒÔµ±a¡Ü0ʱ£¬f¡ä(x)¡Ý0ÔÚRÉϺã³ÉÁ¢£¬ËùÒÔ
f(x)ÔÚRÉϵ¥µ÷µÝÔö£¬f(x)ûÓм«Öµµã£¬²»·ûºÏÌâÒ⣻µ±a>0ʱ£¬Áîf¡ä(x)£½0µÃx£½¡Àa£¬
µ±x±ä»¯Ê±£¬f¡ä(x)Óëf(x)µÄ±ä»¯Çé¿öÈçϱíËùʾ£º
x f¡ä(x) f(x) (£¡Þ£¬£a) £« £a 0 ¼«´óÖµ (£a£¬a) £ a 0 ¼«Ð¡Öµ (a£¬£«¡Þ) £« ?a<2£¬?£a>£1£¬
ÒòΪº¯Êýf(x)ÔÚÇø¼ä(£1£¬2)ÉϽöÓÐÒ»¸ö¼«Öµµã£¬ËùÒÔ?»ò?½â
?£a¡Ü£1?2¡Üa£¬
µÃ1¡Üa<4.Ñ¡C£®
6£®f(x)£½x£3x£«2ÔÚÇø¼ä[£1£¬1]ÉϵÄ×î´óÖµÊÇ________£® ½âÎö£ºf¡ä(x)£½3x£6x£½3x(x£2)£¬ Áîf¡ä(x)£½0µÃx£½0»òx£½2(Éá)£¬ µ±£1 ËùÒÔµ±x£½0ʱ£¬º¯ÊýÈ¡µÃ¼«´óÖµ¼´×î´óÖµ£¬ ËùÒÔf(x)µÄ×î´óֵΪ2. ´ð°¸£º2 7£®ÒÑÖªº¯Êýy£½f(x)£½x£«3ax£«3bx£«cÔÚx£½2´¦Óм«Öµ£¬ÆäͼÏóÔÚx£½1´¦µÄÇÐÏßƽÐÐÓÚÖ±Ïß6x£«2y£«5£½0£¬Ôòf(x)µÄ¼«´óÖµÓ뼫Сֵ֮²îΪ________£® 2 3 2 2 3 2 ??3¡Á2£«6a¡Á2£«3b£½0£¬??a£½£1£¬2 ?½âÎö£ºÒòΪy¡ä£½3x£«6ax£«3b£¬?? 2 ?3¡Á1£«6a£«3b£½£3?b£½0.?? 2 ËùÒÔy¡ä£½3x£6x£¬Áî3x£6x£½0£¬Ôòx£½0»òx£½2. ËùÒÔf(x)¼«´óÖµ£f(x)¼«Ð¡Öµ£½f(0)£f(2)£½4. ´ð°¸£º4 8£®Èôº¯Êýf(x)£½xln x£x£x£«1(a£¾0)ÓÐÁ½¸ö¼«Öµµã£¬ÔòaµÄÈ¡Öµ·¶Î§Îª________£® 22 a2 2½âÎö£ºÒòΪf(x)£½xln x£a2 2x£x£«1(x>0)£¬ ËùÒÔf¡ä(x)£½ln x£ax£¬f¡å(x)£½1 x£a£½0£¬ µÃÒ»½×µ¼º¯ÊýÓм«´óÖµµãx£½1 a£¬ ÓÉÓÚx¡ú0ʱf¡ä(x)¡ú£¡Þ£»µ±x¡ú£«¡Þʱ£¬f¡ä(x)¡ú£¡Þ£¬ Òò´ËÔº¯ÊýÒªÓÐÁ½¸ö¼«Öµµã£¬ Ö»Òªf¡ä??1?a??11? £½lna£1>0£¬½âµÃ0 9£®ÒÑÖªº¯Êýf(x)£½ax2 £bln xÔÚµãA(1£¬f(1))´¦µÄÇÐÏß·½³ÌΪy£½1. (1)ÇóʵÊýa£¬bµÄÖµ£» (2)Çóº¯Êýf(x)µÄ¼«Öµ£® ½â£º(1)f(x)µÄ¶¨ÒåÓòÊÇ(0£¬£«¡Þ)£¬f¡ä(x)£½2ax£bx£¬ f(1)£½a£½1£¬f¡ä(1)£½2a£b£½0£¬ ½«a£½1´úÈë2a£b£½0£¬½âµÃb£½2. (2)ÓÉ(1)µÃf(x)£½x2 £2ln x(x>0)£¬ 2 ËùÒÔf¡ä(x)£½2x£2x£½2x£2 x£¬ Áîf¡ä(x)>0£¬½âµÃx>1£¬Áîf¡ä(x)<0£¬½âµÃ0 (1)Èôº¯Êýf(x)ÔÚÇø¼ä(a£¬a£«1 2 )ÉÏ´æÔÚ¼«Öµ£¬ÇóÕýʵÊýaµÄÈ¡Öµ·¶Î§£» 3