Question

ij¹«Ë¾Éú²ú2010ÄêÉϺ£ÊÀ²©»áµÄ¿Æ¼¼¼ÍÄîÆ·£¬ÒÑÖªÉú²úx£¨x¡ÊN^*£©Íò¼þ¼ÍÄîÆ·µÄÊÕÈ뺯ÊýΪR(x)=

8 x   (0£¼ x£¼9) -x2+16x-39  (9 ¡Ü x¡Ü 15).

£¨µ¥Î»£ºÍòÔª£©£¬Æä³É±¾Óɹ̶¨³É±¾ºÍ¿É±ä³É±¾Á½²¿·Ö¹¹³É£¬ÆäÖй̶¨³É±¾Îª5ÍòÔª£¬¿É±ä³É±¾ÓëÉú²úµÄ¼ÍÄîÆ·µÄ¼þÊýx³ÉÕý±È£¬ÓÖÖª¸Ã¹«Ë¾Éú²ú10Íò¼þ²úƷʱ£¬»¨·ÑµÄ¿É±ä³É±¾Îª20ÍòÔª£®£¨ÀûÈó=ÊÕÈë-³É±¾£©
£¨1£©ÇóÀûÈóº¯ÊýP£¨x£©£»
£¨2£©µ±Éú²ú¶àÉÙÍò¼þ¼ÍÄîƷʱ£¬¸Ã¹«Ë¾Äܹ»È¡µÃ×î´óÀûÈ󣿲¢Çó³ö×î´óÀûÈó£®

Answer 1

·ÖÎö£º£¨1£©ÏÈÇó³ö¹«Ë¾µÄ³É±¾º¯ÊýC£¨x£©£¬È»ºóÈóº¯ÊýP£¨x£©=R£¨x£©-C£¨x£©·Ö¶Î½øÐÐÇó½â¼´¿É£»
£¨2£©·Ö¶Î·Ö±ðÇó³öº¯ÊýµÄ×î´óÖµ£¬ÓÉÀûÈóº¯ÊýÊǶþ´Îº¯Êý»ò¿Éת»¯³É¶þ´Îº¯Êý£¬¿ÉÒÔÀûÓöþ´Îº¯ÊýµÄÐÔÖÊÇó³öº¯ÊýÈ¡×î´óֵʱ¶ÔÓ¦µÄ×Ô±äÁ¿xµÄÖµ£®

½â´ð£º½â£º£¨1£©Éè¸Ã¹«Ë¾Éú²ú¼ÍÄîÆ·µÄ¿É±ä³É±¾ÎªS£¨x£©ÓÉÌâÒâ¿ÉÉè S£¨x£©=kx£¨k£¾0£©
ÓÖÖª¸Ã¹«Ë¾Éú²ú10Íò¼þ²úƷʱ£¬»¨·ÑµÄ¿É±ä³É±¾Îª20ÍòÔª
ËùÒÔ  20=10kµÃ k=2
ÓÉÆä¹Ì¶¨³É±¾Îª5ÍòÔª£¬µÃ
¸Ã¹«Ë¾µÄ³É±¾º¯ÊýC£¨x£©=2x+5¡­£¨3·Ö£©
ÒòΪÊÕÈ뺯ÊýΪR(x)=

8 x   (0£¼ x£¼9) -x2+16x-39  (9 ¡Ü x¡Ü 15).

ËùÒÔ£¬µ±0£¼x£¼9ʱ£¬ÀûÈóº¯ÊýP£¨x£©=R£¨x£©-C£¨x£©=8

x

-(2x+5)=-2x+8

x

-5
µ±9¡Üx¡Ü15ʱ£¬ÀûÈóº¯ÊýP£¨x£©=R£¨x£©-C£¨x£©=£¨-x²+16x-39£©-£¨2x+5£©=-x²+14x-44
ËùÒԸù«Ë¾Éú²ú¼ÍÄîÆ·µÄÀûÈóº¯ÊýΪP(x)=

-2x+8 x -5  (0£¼ x£¼9£¬x¡ÊN*) -x2+14x-44  (9 ¡Ü x¡Ü 15£¬x¡ÊN*).

¡­£¨8·Ö£©
£¨2£©µ±0£¼x£¼9ʱ£¬P(x)=-2x+8

x

-5=-2(

x

-2)2+3
ÒòΪ0£¼x£¼9£¬x¡ÊN^*
ËùÒÔ£¬µ±

x

=2¼´x=4ʱ£¬P£¨x£©µÄ×î´óֵΪ3ÍòÔª£»¡­£¨11·Ö£©
µ±9¡Üx¡Ü15ʱ£¬P£¨x£©=-x²+14x-44=-£¨x-7£©²+5ÔÚÇø¼ä[9£¬15]Ϊ¼õº¯Êý£¬
µ±x=9ʱ£¬P£¨x£©=1¡­£¨14·Ö£©
ËùÒÔ£¬µ±9¡Üx¡Ü15ʱ£¬P£¨x£©×î´óֵΪ1ÍòÔª£®
´ð£ºµ±x=4Íò¼þʱ£¬ÀûÈóµÄ×î´óֵΪ3ÍòÔª£®¡­£¨16·Ö£©

µãÆÀ£º±¾ÌâÔÚÕýÈ·Àí½âÀûÈóº¯ÊýµÄ»ù´¡ÉÏ£¬ÔËÓöþ´Îº¯ÊýµÄÐÔÖÊ£¬½â¾öʵ¼ÊÓ¦ÓÃÎÊÌ⣬½âÌâµÄ¹Ø¼üÊǷֶκ¯ÊýÐè·Ö¶ÎÇó£¬ÊôÓÚ»ù´¡Ì⣮