.
, , .. , n . n , ? , , . , , , , . , , .
, (x1,x3) f(x2) (. . 3). 4, 4, ?
.3.
21=L 32=R, L > R, . 3, , x1, x2 3. 4 (1; 2), :
1. f(x4) < f(x2), (x1,x2) 21=L;
2. f(4)>f(x2), (4,3) 34.
, , 4 , 3-4 2-1. , 3 4 2 1 .. 4 2, . 4 , L. 4 2, . , , (1, 2), , 4, (4,3), , 2.
, . . , , , , , .
n - n - (n 1) - . . , . n-1. . n-1 n , , , , . /2 Ln-1; .
|
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Ln, , Ln-1 = 2Ln - (.4), ). n-1 n-2 Ln-2 Ln-2 . , Ln-2 = Ln-1+Ln (p.4, ).
. 4.
. , n-2 .
Ln-3=Ln-2+Ln-1 (p. 4, )
Lj-1=Lj + Lj+1 1<j<n.
,
: F0=1, F1=l, Fk=Fk-1+Fk-2 k = 2, 3,...,
(1) |
(a;b) L = (b-),
(2) |
, n , l/Fn ( ), - .
, , . , , L2 , , , a L2 :
(3) |
, . . L1\Fn+x, .
, , , . (x1; x2) 2, , 2 , 34 = 21 4-1 = 3-x2, .. x4=1-2+3.
f(x2) = f2 f(x4) = f4, (. 5).
.5.
" ".
, . L2, .. (. 3).
" " , , n - , . j , , (. 1),
(4) |
n , Ln-1 = Ln - . , ..
(5) |
..
, , .
, , ..
(6) |
, . , . L1/t , - .
(3) , " " . " " (5). , Lj-1 , , .. " ".
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, (0, 3) f1 f2 x1 x2, (. 6).
. 6.
, .
" " .7
. 7. " ".
c - ,
x - , F(x) ( ), FM F(x) .
. . .
( ), F(x), f(x).
, F(x) ( ) , F(x) ( ) , ..
, F(x) ,
(7) |
. - (3.1), , , F'(x)=0, F(x) ( ) (.8).
. 8. F(x) f(x).
f(x) (7).
f(x) :
hi=xi+1-xi.
, .
:
(xi+1) F(x), f(xi+1)=0.
:
(8) |
F(x) F1 F2 F(x), ..
[a,b], f(x) f''(x) , ..
(9) |
:
1. . , x=a, x=b.
2. (xi+1) (8).
3. ,
(10) |
(8) (10)
(8)
.
F(x) , , .. , , (. 9 a).
F(x) , , .. , , (. 9 b).
, : F(x).
. 9.
F(x) , F(x) :