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(2 - )

, . :

a, b f . < b f(a) < f(b) ( f(a) > f(b) ) f () .

12

v - (x) > 0 ((x) < 0) f () .

(x) > 0 v, 㺺 . a, b a < b 11-

- . (a, b) . (x) > 0

. b - a > 0 f(b) - f(a) > 0 .

max, min (x) = 0 . - f - max - , min - ? - . - max (min) - ? :

f max - . v v - max. ( ) min - ( , vv !). , . (x) = 0 . , .

f(x) = anxn + an-1xn-1 + ...+ a0 v. . n - v. vv .

1, x2 , f(x1)=f(x2)=0 , 10 - 1, x2 (x) = 0 - . f (1< x2< ... < xk) -1 . . n = 1 . g' n - v , g n + 1 - v. , g n+1 - g' n - .

vv v. v . vv v . ,

=1 v . ? . f - :

. = 0, 2 . a o. f(0) = -2, f(2) = 2. , . 12- , vv vv , :

v: --> (x ), -->- ( ), -->1 ( ) - ?

--> f(x)-->, -->- f(x)-->- v. ( , 1/(x-1) , v v ).

. 1- , (-1) . ( f(x) , .) :

v . f(x) 2 min, 0 max - .

v , .

13

(a)=0 . ()>0 (()<0) f min (max) - .

,

() > 0 .

1. h+-->0 (a+h) .
2. h--->0 (a+h) .

f 12- - vv , - v . - min - . () < 0 㺺 .

... () > 0 () . ()=0 , , () - vv , - . f - , - vv .

<-- (1) | vv | (3)-->


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