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à¤Ã×èͧÁ×ͧ͢ËÑÇ¢éÍ | ¤é¹ËÒã¹ËÑÇ¢é͹Õé |
#1
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ËҨشÊÙ§ÊØ´-µèÓÊØ´ÊÑÁ¾Ñ·¸ì
»¡µÔàÃÒ¨ÐËҨشÊÙ§ÊØ´-µèÓÊØ´ÊÑÁ¾Ñ·¸ì¢Í§¿í§¡ìªÑ¹ f:R->R â´Â¡ÒÃËÒ͹ؾѹ¸ì¢Í§ f áÅéÇËҨشÇԡĵ (critical points) ¨Ò¡¹Ñé¹ÁÒÇÔà¤ÃÒÐËìµèͨش´Ñ§¡ÅèÒÇà»ç¹¨Ø´ÊÙ§ÊØ´-µèÓÊØ´ÊÑÁ¾Ñ·¸ì
»ÑËÒ¤×Í ¶éÒ f:R->R ËÒ͹ؾѹ¸ìäÁèä´é·Ñé§ËÁ´º¹ R ¨Ð·ÓÍÂèÒ§äà àªè¹ f(x)=|x| àÁ×èÍ xÎR ·ÓÍÂèÒ§äèÐä´éÇèÒ ¨Ø´µèÓÊØ´ÊÑÁ¾Ñ·¸ì¤×Í (0,0) |
#2
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¤×ÍäÁèà¢éÒ㨤ӷÕèÇèÒ ËÒ͹ؾѹ¸ìäÁèä´é·Ñé§ËÁ´º·¨Ó¹Ç¹¨ÃÔ§ ÂѧäÁèà¤ÂàË繿ѧ¡ìªÑ¹áºº¹Õé áµèÅͧ´Ù¤Ó͸ԺÒ¹Õé´Ù
¶éÒàÃÕ¹ÁÒã¹Á.»ÅÒ ¨Ø´Çԡĵ ¨ÐÁÕ੾ÒШش·Õè·ÓãËé f'(c)=0 ÍÂèÒ§à´ÕÂǨԧæ äÁèãªè ·Ñé§ËÁ´
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PaTa PatA pAtA Pon! |
#3
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¢Íâ·É¤ÃѺ¶éÒ¤Ó¶ÒÁäÁèªÑ´à¨¹
»ÑËÒ¤×Í ¶éÒ f:R->R ËÒ͹ؾѹ¸ìäÁèä´é·Ñé§ËÁ´º¹ R ¨Ð·ÓÍÂèÒ§äà àªè¹ f(x)=|x| àÁ×èÍ xÎR ·ÓÍÂèÒ§äèÐä´éÇèÒ ¨Ø´µèÓÊØ´ÊÑÁ¾Ñ·¸ì¤×Í (0,0) à¾ÃÒÐÇèÒàÃÒ¨ÐãªéÇÔ¸Õà´ÔÁ æ ·ÕèÁÕÍÂÙèÇÔà¤ÃÒÐËìäÁèä´é |
#4
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¡çËÒ¨Ò¡¨Ø´Çԡĵ µÒÁ¹ÔÂÒÁ·Õè M@gpie ãËéäÇé䧤ÃѺ.
â´Â·ÑèÇ仡ÒÃËÒ¤èÒµèÓÊØ´ÊÙ§ÊØ´ÊÑÁ¾Ñ·¸ì º¹ªèǧ [a, b] ¨Ð¾Ô¨ÒóҨҡ 1. f(a), f(b) 2. f(c) àÁ×èÍ c à»ç¹¨Ø´Çԡĵ µÒÁ¹ÔÂÒÁ·ÕèÇèÒäÇé ¤×Í f'(c) = 0 ËÃ×Í f'(c) ËÒ¤èÒäÁèä´é ¶éҿѧ¡ìªÑ¹·Õèµéͧ¡ÒÃËÒ͹ؾѹ¸ìäÁèä´é§ËÁ´ ÍÂèÒ§äáç´Õ¡çµéͧËÒ͹ؾѹ¸ìä´éà»ç¹ªèǧ æ «Ö觵çÃÍÂÍÒ¨¨ÐËÒ͹ؾѹ¸ìäÁèä´é ÍÂèÒ§äáç´ÕµÃ§Ã͵èÍ¡ç¨Ðà»ç¹¢Íºáºº ¢éÍ 1. ¶éÒÂѧäÁèà¤ÅÕÂÃìÅͧ¡µÑÇÍÂèÒ§Í×è¹ æ ´Õ¡ÇèÒ¤ÃѺ. |
#5
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ãËé f:[0,1]->R ¹ÔÂÒÁ´Ñ§¹Õé f(0)=0,
f(x)=(1/(2^n))x ¶éÒ xÎ[1/(2^{n+1}),1/(2^n)] àÁ×èÍ n=0,1,... ¨Ø´ÇԡĵàµçÁä»ËÁ´àÅ µéͧÁÒ¤Ô´àµçÁä»ËÁ´ Ẻ¹Õéà»ç¹µé¹ |
#6
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㹡óÕàªè¹¹ÕéÅͧÇÒ´ÃÙ»´ÙáÅéÇ ¡ÃÒ¿Áѹà»ç¹àÊ鹵ç áµèäÁèµèÍà¹×èͧ¡Ñ¹ áµè¡çÊÒÁÒöËÒ͹ؾѹ¸ìä´éà»ç¹ªèǧ æ «Öè§ã¹·Õè¹Õé¡çäÁèÁÕ»ÃÐ⪹ìÍÐäà à¾ÃÒж×ÍÇèÒ äÁèÁÕ¤èÒÊÙ§ÊØ´ËÃ×͵èÓÊØ´ÊÑÁ¾Ñ·¸ì ÁÕáµè¤èÒÊÙ§ÊØ´ÊÑÁºÙÃ³ì ¤×Í 1 à¡Ô´àÁ×èÍ x = 1 Êèǹ¤èÒµèÓÊØ´ÊÑÁºÙóì¨ÐäÁèÁÕ ¶éÒäÁè¡Ó˹´ÇèÒ f(0) = 0 㹡óչÕé¡Ó˹´ÁÒãËé «Ö觵èÓÊØ´¨ÃÔ§ æ ¨Ö§ÁÕ¤èÒµèÓÊØ´ÊÑÁºÙóìà»ç¹ 0
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