¥Ñ benice ©ó ¬P´Á¤é ¤»¤ë 22, 2014 6:49 pm
1.
©_¨ç¼Æ©w¸q©Ê½è¬° f(-x) = -f(x)¡C
¦pªG 0 ¦b©w¸q°ì¤º¡A¨º»ò f(-0) = -f(0) ¥i±À±o f(0) = 0¡C
¦Ò¼{ f(x) = sin(1/x), x¡Ú0¡A
«h f(-x) = sin(1/(-x)) = sin(-1/x) = -sin(1/x) = -f(x)¡C
©Ò¥H¨ç¼Æ f ¦b¨ä©w¸q°ì (-¡Û,¡Û)/{0} ¤º¬°©_¨ç¼Æ¡C
¦pªG¦Ûq¤@¨ç¼Æ g¡G
g(x) =
ùúsin(1/x), if x¡Ú0
¢x
ùü0, if x=0
«h g ¦b¨ä©w¸q°ì (-¡Û,¡Û) ¤º¤]¬O©_¨ç¼Æ¡C
¦ý¦pªG¦Ûq¥t¤@¨ç¼Æ h¡G
h(x) =
ùúsin(1/x), if x¡Ú0
¢x
ùü1, if x=0
«h h ¦b¨ä©w¸q°ì (-¡Û,¡Û) ¤º¤£¬O©_¨ç¼Æ¡C
©_¨ç¼Æ¤£¤@©wn³sÄò¡A¨Ò¦p±`¥Îªº²Å¸¹¨ç¼Æ sign¡G
sign(x) =
ùú 1, if x>0
¢x 0, if x=0
ùü -1, if x<0
ÁöµM sign ¦b x=0 ³B¤£³sÄò¡A¦ý¦b¨ä©w¸q°ì (-¡Û,¡Û) ¤º¬°©_¨ç¼Æ¡C
2.
¤T¦¸¨ç¼Æ¤§¤@¯ë¦¡¬° f(x) = ax³ + bx² + cx + d, (a¡Ú0)¡C
·L¤À±o
f'(x) = 3ax² + 2bx + c
f"(x) = 6ax + 2b
f"(x) = 0 => x = -b/(3a)
¥O x0 = -b/(3a)
¦]¬° f" ¬°¹Ï§Î«D¤ô¥½uªº½u©Ê¨ç¼Æ(¡î 6a¡Ú0)¡A
©Ò¥H x0 ¬°°ß¤@ªº x Ȩϱo f" ¦b x0 ¨â°¼¬°²§¸¹ (¨£¥H¤U¸Ô²Ó»¡©ú)¡A
§Y (x0,f(x0)) ¬° f °ß¤@¤§¤Ï¦±ÂI¡C
¬G¤T¦¸¨ç¼Æ¥²¦³¤@°ß¤@ªº¤Ï¦±ÂI¦s¦b¡C
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Y a¡Õ0¡A«h¡G
·í x¡Öx0 ®É¡Af"(x) «í¤p©ó¹s
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