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: , vv v . (f(x)=x2 vv ?) F(x) . . F(x) vv v. F - ?

- (1- )

[a, b] f . . f [a, b] c v F(c) c F'(c)=f(c).

c=a, =b v (a, b) .

. h > 0

.

mh = inf {f(x) : c x c+h}
Mh = sup {f(x) : c x c+h}

25-

. h<0 (1) . f c v ,

. F'(c) f(c) (vv ), ( vv ) F'(c)=f(c) !

v v . F(x) f vv, vv v F - , " " f - .

.

G'(c) = -f(c) . x<a vvv F

. , <a F'(c) = -(-f(c)) = f(c) , c<a v .

v. 1- .

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f [a, b] 㺺, f=g'

: f [a, b] v v . ( v.) v f [a, b] . ( .)

[a, b] P . 11- [ti-ti-1]

vv xi .

mh = inf {f(x) : c x c+h}
Mh = sup {f(x) : c x c+h}

. i=1,...,n - v

. , L(f,P) g(b) - g(a) U(f,P) .

: vv! f 㺺 . ( f(x) = {x=1 1, 0 0}.)

v , vvv. x2 ... g'(x)=x2 . g(x)=x3/3+c . (c v .) c - , c - v. - (..)

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. g(x) v v .

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. F(x) v . 8- . :

(8- ), v.

v .

27

[a, b] v f . f [a, b] .

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