, , . , '. '.
2.1. '
(2.1) |
( + ) + ( -) = 2
'
:
,
(2.2)
' (2.2)
. (2.3)
, , ' (2.1) , (2.3).
, , , ' (2.1).
ij,
2.2. '
(2.4)
'. (2.4) :
' (2.5) ,
(2.6)
(2.6) (2.4), .
' (2.1) (2.4) ,
2.3. '
(2.7)
' (2.8) = = 0,
= 0, = ,
(2.)
= 0 (2.8)
-
(2.9)
ϳ (2.8) = 2,
(2.10) ,
(2.8)
>1 , , , , >1, (2.10),
, .
3
x = F (x), , , F (x), . , f (x) = 0.
. , - , , .
, .
1. , x = x0 f(x) x0, x0, f(x) > f (x0) x > x0, f (x) < f (x0) x < x0 ( f (x) < f (x0) x > x0, f (x) > f (x0) x < x0).
|
|
1. f (x) x0 f '(x0) > 0 ( f'(x0) < 0), f (x) x0.
f'(x0) > 0 ( f '(x0) < 0 ). f '(x0), , x > x0 , x0 (1) f '(x0), f '(x0) > 0, x0 (1) . , f (x) - f (x0) > 0 x x0 > 0 f(x)- f (x0) < 0 x x0 <0 , , f (x) > f (x0) x > x0 f (x) < f (x0) x < 0.
.
2. , x = x0 f (x) x0 ( ), x0, f (x0) ( ) f (x) .
2. f (x) x0 , ' f '(x0) = 0.
, f (x), x0 , x0 , . , 1 f '(x0) , 䒺, f '(x0) = 0. .
3. , f (x) x0, x0 f (x0) .
3 ( ). f (x) [;b] , , f (a) = f (b), x, f '(x) .
, ... : f (x) [a;b], x0, f(x0) f (x) , x1, f (x1) f (x) .
3, , f (x) [ a; b], x f (x) = f (a) = f (b).
f '(x) - x [a;b]. f (x) [a;b]. x f (x) f (a). f (x) > f (a). f (x) x f (x) x . 2 f '(x) = 0.
.
4. 4 ( ). f (x) [a;b] , x, , , :
f (b) - f (a) = f '(x)(b - a)
[a;b] , 3. ij, f (x) [a;b] ( f (x) ) . (3) , f (a) = f (b) = 0. 3 [a;b] x, , f (a) = f (b) = f(x)(b-a)
|
|
.