: f
2015 : f
x1, x2 A x1 < x2 f(x1)f(x2)
: f
x1, x2 A x1 < x2 f(x1)=f(x2)
: f x0A , xATo f(x0) f , x0 (x0,f(x0)) .
: f x0A , xATo f(x0) f , x0 (x0,f(x0))
: f x0A >0 , f(x) f(x0) , x(x0- , x0+)
: f x0A >0 , f(x)f(x0) , x(x0- , x0+) ( ...) f :
[, ]
(, )
, , (, ), :
: f(x) f(x)> 0 , f . f (x) > 0.
x1x2 x1< x2. f(x1) < f(x2). , [x1,x2] f ... , (x1,x2) ,
,
f(x2)f(x1)=f ()(x2x1)
f () > 0 x2 x1> 0, f(x2) f(x1) > 0, f(x1) <
f(x2).
f ' x0 . f x0 , :
f (x0) = 0
f x0 . x0 f ' , > 0 ,
(x0 , x0+ )
f(x) f(x0) x (x0 , x0+ ) . (1)
, , f x0,
,
x (x0 , x0), (1), ,
x (x0, x0+ ), (1), ,
, (2) (3) f (x0) = 0.
: F f :
F(x) = f(x) , . F (x)= A :
1,2,...,. 1 1 2 2 ,, , 12.... , , .
M .
. .
Laplace , Laplace 1812.
:
1. 2. 3. 0 P(A) 1, .
: ()>0. , (|), (4)
:
:
:
, . 1. :
N(A) =N(B) = , AUB +, . ,N(AUB)=+=N(A)+N(B).:
2. A' :
AA' = , A' , , :
P(A') = 1 - P(A).
3. :
N(AUB) = N(A) + N(B) - N (A B), (1) N(A) + N(B) AB . (1) N()
:
P(AUB) = P(A) + P(B) - P(AB). (additive law).
4.
A B :
5.
P(A-B) = P(A) - P(AB).
A-BAB (A-B)U(AB) = A, :
P(A) = P(A - B) + P(AB).
P(A-B) = P(A) - P(AB).
.
(1,1) 2+2+2g+2f+c=0 12+12+2g1+2f1+c. . : SOS . C Latus rectum: '
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