1、BACCBKBDA4B4BRCIA11 A0B4CCBK f(x) D6 (a,b) B6AYAYDEBAA5D7 (a,b) DJBDBICKD9C0f(x)BDA3CKBIA5CKD9C0BHBSDHCTBPBIA1DBAIA1CTC0f(x)AYAYDEBAA5BQB1CS x0 (a,b),f(x0) = f+(x0) = limxx0+f(x)f(x0)xx0limxx0+f(x0 + x)(xx0)xx0 = limxx0+f(x0 + x),C6f(x)D6x0 B2D6CYCMC9BAA5COBJCXf(x0) = f(x0 + 0).f(x0) = f(x0) = limxx
2、0f(x)f(x0)xx0limxx0f(x0 + x)(xx0)xx0 = limxx0f(x0 + x).1C6f(x)D6x0 B2D6ACCMC9BAA5COBJCXf(x0) = f(x0 0).CND6BHA5B4f(x)D6x0 B2D6ACCYCMC9BAA5D6x0 COBJA3CKA1B4CXCOAOCMC9ALB2D6A5D7C0BHBSDHCTBPBIA12A0G.DarbouxBJDIB4CCBK f(x)D6a,bDEBAA5 f(a) nsummationdisplayi=1kif(xi).DBAXx0 =nsummationdisplayi=1kixi A5CX
3、f(xi)D6x = x0 AYD8DAf(xi) = f(x0)+f(x0)(xix0)+12f(i)(xix0)2 f(b)DHBMDEDB)A1CQc = a + b2 A1B4f(c) f(a) + f(b)2 A5CWA32)BEDEDC|f(b)f(a)| = f(b)f(a) 2f(c)f(a) = f()(ba2 )2BOCQ|f()| 4(ba)2|f(b)f(a)|,B4f(c) 0, (2)BRM0hhM22 =12M0M2 C0APBKA1BOCQA32A4BECYBOC0hBDCCBKBAA515B9M0h =hM22 AXABCDA1A9 h =2radicalbi
4、gg2M0M2 A5B6B3BC |f(x)| 2M0M2,x (,+)A5BOCQM21 2M0M2.A13.3.10B9CCBKf(x)D6(,+)B6CXB5CZBABKA5AKASf(x)CDf(x)D6(,+)B6CXD2A1DBAIA7f(x)CDf(x)CND6(,+)B6CXD2A1AXh = 1BCf(x + 1) = f(x) + f(x) + 12f(x) + 13!f(), (1)f(x1) = f(x)f(x) + 12f(x) 13!f(), (2)A31A4-(2)BCf(x + 1)f(x1) = 2f(x) + 13!f() + f()16BOCQ2|f(x)
5、| 2M0 + 13M3,x (,+),Mk = sup 0, 0, B917x BA|(x)| 0,(x+ h) = (x) + (x)h + 12()h2,CO(x) = 1h(x + h)(x) 12()h, (1)CQ A = limx+(x) A1CT (x) CXD2A5BOCQ M 0 A5BCBC|(x)| M(x a)A1C6CWA31A4DC|(x)| 1h(|(x + h)A|+|A(x)|) + 12Mh2, (2) 0,BJC8DEAXh 0AVBVCDA5BCBC12Mh2 0,B9 x A51h(|(x + h)A|+|A(x)|) 0;A32A4B9k = 2,
6、3,(n1)BAA5CXf(k)(x0) = 0B8BHf(n)(x0) negationslash= 0;A33A4B90 negationslash= |h| 0 A5BCBC (,) AL f(x) 0. DBC0A5DBAI f(x) D625x = 0BDA7D2ALCFC0A8A1C3CX (1)BECYBOBDf(x), f(x)D6x = 0AYA9TaylorC3BED8DAA1A6CSBB f(0) = f(0) = 0,C3CXf(x) = f(0) + f(0)x + f()2 x2,f(x) = f(0) + f()x = f()x.B1BR|f(x)|+|f(x)|
7、 = |12f()x2|+|f()x|.D4C9DH x 14, 14 A5D7 |f(x)| + |f(x)| D6 14, 14 B6A3CKCX x0 14, 14A5BCBC|f(x0)|+|f(x0)| = max14 x14|f(x)|+|f(x)| m,C3DFCMDBAI M = 0CODEA1BGBBB6M = |f(x0)|+|f(x0)| = |12f(0)x0|+|f(0)x0|26 14|f(0)|+|f(0)| 14(|f(0)|+|f(0)|+|f(0)|+|f(0)|) 142M = 12M.CO0 M 12M.BOCQM = 0A5D614, 14B6f(x) 0A5DBA127
