ÒòΪh(x)£½nxÔÚ(£¡Þ,£«¡Þ)Éϵ¥µ÷µÝÔö,ÇÒh(x1¡ä)£½a£½f(x1)£¼h(x1),Òò´Ëx1¡ä£¼x1. Óɴ˿ɵÃx2£x1£¼x2¡ä£x1¡ä£½ÒòΪn¡Ý2,ËùÒÔ2¹Ê2¡Ýnn£1
£«x0. 1£n¡Ý1£«Cn£1£½1£«n£1£½n,
1
a£½(1£«1)
n£1
1a£½x0.ËùÒÔ,|x2£x1|£¼£«2. n£11£n2a2
17.½â (1)f¡ä(x)£½3x£«2ax,Áîf¡ä(x)£½0,½âµÃx1£½0,x2£½£. 3
µ±a£½0ʱ,ÒòΪf¡ä(x)£½3x£¾0(x¡Ù0),ËùÒÔº¯Êýf(x)ÔÚ(£¡Þ,£«¡Þ)Éϵ¥µ÷µÝÔö£» 2a???2a?µ±a£¾0ʱ,x¡Ê?-¡Þ£¬-?¡È(0,£«¡Þ)ʱ,f¡ä(x)£¾0,x¡Ê?-£¬0?ʱ,f¡ä(x)£¼0,ËùÒÔº¯Êý3???3?2a???2a?f(x)ÔÚ?-¡Þ£¬-?,(0,£«¡Þ)Éϵ¥µ÷µÝÔö,ÔÚ?-£¬0?Éϵ¥µ÷µÝ¼õ£»
33
2
????
2a??2a??µ±a£¼0ʱ,x¡Ê(£¡Þ,0)¡È?££¬£«¡Þ?ʱ,f¡ä(x)£¾0,x¡Ê?0£¬£?ʱ,f¡ä(x)£¼0,ËùÒÔº¯
3??3??2a??2a??Êýf(x)ÔÚ(£¡Þ,0),?££¬£«¡Þ?Éϵ¥µ÷µÝÔö,ÔÚ?0£¬£?Éϵ¥µ÷µÝ¼õ.
3??3??
?2a?43
(2)ÓÉ(1)Öª,º¯Êýf(x)µÄÁ½¸ö¼«ÖµÎªf(0)£½b,f?£?£½a£«b,Ôòº¯Êýf(x)ÓÐÈý¸öÁãµãµÈ
?3?27
a£¾0£¬a£¼0£¬????2a4???3?¼ÛÓÚf(0)¡¤f?£?£½b?a£«b?£¼0,´Ó¶ø?43»ò?43
?3??27?£a£¼b£¼00£¼b£¼£a.??27?27?
4343
ÓÖb£½c£a,ËùÒÔµ±a£¾ 0ʱ,a£a£«c£¾0»òµ±a£¼0ʱ,a£a£«c£¼0.
272743
Éèg(a)£½a-a£«c,ÒòΪº¯Êýf(x)ÓÐÈý¸öÁãµãʱ,
27
aµÄȡֵ·¶Î§Ç¡ºÃÊÇ(-¡Þ,-3)¡È?1£¬?¡È?£¬£«¡Þ?,
22
??
3??3
??
??
?3??3?ÔòÔÚ(-¡Þ,-3)ÉÏg(a)£¼0,ÇÒÔÚ?1£¬?¡È?£¬£«¡Þ?ÉÏg(a)£¾0¾ùºã³ÉÁ¢. ?2??2??3?´Ó¶øg(£3)£½c£1¡Ü0,ÇÒg??£½c£1¡Ý0,Òò´Ëc£½1. ?2?
´Ëʱ,f(x)£½x£«ax£«1£a£½(x£«1)[x£«(a£1)x£«1£a],
Òòº¯ÊýÓÐÈý¸öÁãµã,Ôòx£«(a£1)x£«1£a£½0ÓÐÁ½¸öÒìÓÚ£1µÄ²»µÈʵ¸ù, ËùÒÔ¦¤£½(a-1)£4(1-a)£½a£«2a-3£¾0, ÇÒ(-1)-(a-1)£«1-a¡Ù0,
2
2
2
2
3
2
2
?3??3?½âµÃa¡Ê(-¡Þ,-3)¡È?1£¬?¡È?£¬£«¡Þ?.×ÛÉÏc£½1. ?2??2?
17
18.½â
2
(1)¶Ôf(x)Çóµ¼µÃ
£¨6x£«a£©e££¨3x£«ax£©e
f¡ä(x)£½£½x2
£¨e£©
x2x£3x£«£¨6£a£©x£«a, xe
ÒòΪf(x)ÔÚx£½0´¦È¡µÃ¼«Öµ,ËùÒÔf¡ä(0)£½0,¼´a£½0.
3x£3x£«6x33
µ±a£½0ʱ,f(x)£½x,f¡ä(x)£½,¹Êf(1)£½,f¡ä(1)£½,´Ó¶øf(x)ÔÚµã(1,f(1))´¦xeeee33
µÄÇÐÏß·½³ÌΪy££½(x£1),»¯¼òµÃ3x£ey£½0.
ee£3x£«£¨6£a£©x£«a(2)ÓÉ(1)Öªf¡ä(x)£½. xeÁîg(x)£½£3x£«(6£a)x£«a,
6£a£a£«366£a£«a£«36
ÓÉg(x)£½0½âµÃx1£½,x2£½. 66µ±x£¼x1ʱ,g(x)£¼0,¼´f¡ä(x)£¼0,¹Êf(x)Ϊ¼õº¯Êý£» µ±x1£¼x£¼x2ʱ,g(x)£¾0,¼´f¡ä(x)£¾0,¹Êf(x)ΪÔöº¯Êý£» µ±x£¾x2ʱ,g(x)£¼0,¼´f¡ä(x)£¼0, ¹Êf(x)Ϊ¼õº¯Êý.
6£a£«a£«369
ÓÉf(x)ÔÚ[3,£«¡Þ)ÉÏΪ¼õº¯Êý,Öªx2£½¡Ü3,½âµÃa¡Ý£,
62
2
2
2
2
2
2
2
?9?¹ÊaµÄȡֵ·¶Î§Îª?££¬£«¡Þ?.
?2?
19.½â (1)ÉèÇúÏßy£½f(x)ÓëxÖáÏàÇÐÓÚµã(x0,0),Ôòf(x0)£½0,f¡ä(x0)£½0.¼´1??x30£«ax0£«£½0£¬
4 ?
??3x20£«a£½0£¬
133
½âµÃx0£½,a£½£.Òò´Ë,µ±a£½£Ê±,xÖáΪÇúÏßy£½f(x)µÄÇÐÏß.
244
(2)µ±x¡Ê(1,£«¡Þ)ʱ,g(x)£½£ln x<0,´Ó¶øh(x)£½min{f(x),g(x)}¡Üg(x)<0, ¹Êh(x)ÔÚ(1,£«¡Þ)ÎÞÁãµã.
55
µ±x£½1ʱ,Èôa¡Ý£,Ôòf(1)£½a£«¡Ý0,h(1)£½min{f(1),g(1)}£½g(1)£½0,¹Êx£½1ÊÇh(x)
445
µÄÁãµã£»Èôa<£,Ôòf(1)<0,h(1)£½min{f(1),g(1)}£½f(1)<0,¹Êx£½1²»ÊÇh(x)µÄÁãµã.
4µ±x¡Ê(0,1)ʱ,g(x)£½£ln x>0.ËùÒÔÖ»Ð迼ÂÇf(x)ÔÚ(0,1)µÄÁãµã¸öÊý.
(¢¡)Èôa¡Ü£3»òa¡Ý0,Ôòf¡ä(x)£½3x£«aÔÚ(0,1)ÎÞÁãµã,¹Êf(x)ÔÚ(0,1)µ¥µ÷.¶øf(0)£½15
,f(1)£½a£«,ËùÒÔµ±a¡Ü£3ʱ,f(x)ÔÚ(0,1)ÓÐÒ»¸öÁãµã£»µ±a¡Ý0ʱ,f(x)ÔÚ(0,1)ûÓÐÁãµã. 44
18
2
(¢¢)Èô£3 ?? £?µ¥µ÷µÝ¼õ,ÔÚ?3?? a?? ££¬1?µ¥µ÷µÝÔö,¹ÊÔÚ(0,1)ÖÐ,µ±x3? a? £Ê±,f(x)È¡µÃ×îСֵ,×îСֵΪf?3? a? a?2a£?£½3?3 a1££«. 34 ¢ÙÈôf?¢ÚÈôf?¢ÛÈôf??????? 3a?£?>0,¼´£ 43? 3a?£?£½0,¼´a£½£,Ôòf(x)ÔÚ(0,1)ÓÐΨһÁãµã£» 43? 31553a? £?<0,¼´£3 444443? 5 ÓÐÁ½¸öÁãµã£»µ±£3 435 ×ÛÉÏ,µ±a>-»òa<-ʱ,h(x)ÓÐÒ»¸öÁãµã£» 4435 µ±a£½-»òa£½-ʱ,h(x)ÓÐÁ½¸öÁãµã£» 4453 µ±- ¦Ð¦Ð2 20.½â (1)f(sin x)£½sin x£asin x£«b£½sin x(sin x£a)£«b,£ 22¦Ð¦Ð [f(sin x)]¡ä£½(2sin x£a)cos x,£ ÒòΪ£ 22¢Ùa¡Ü£2,b¡ÊRʱ,º¯Êýf(sin x)µ¥µ÷µÝÔö,ÎÞ¼«Öµ. ¢Úa¡Ý2,b¡ÊRʱ,º¯Êýf(sin x)µ¥µ÷µÝ¼õ,ÎÞ¼«Öµ. ?¦Ð¦Ð?¢Û¶ÔÓÚ£2 ?22? ¦Ð