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1. f (x) () (a; b), - x1 x2

(A; b), a?x12?b, AB , A = (x1, F (x1)), B = (x2, F (x2)), . .

f (x1+ T (x2-x1)) ?f (x1) + T (f (x2) - f (x1)), t ? [0; 1]. (5.28)

2. f (x) () (a; b), - x1 x2

(A; b), a?x12?b, AB , . . f (x1+ T (x2-x1)) ?f (x1) + t (f (x2-f (x1)), T? [0; 1].

18. f (x) (a; b) , - x1 x2 (a; b)

f (x2) ?f (x1) + F '(x1) (X2- x1) (5.29)

.. (5.28) (f (x1+ T (x2-x1)) - F (x1)) / T?f (x2) -f (X1).

t > +0.

limt> + 0(F (x1+ T (x2- x1)) - F (x1)) / T = limt> + 0(F (x1+ T (x2- x1)) - F (x1)) / T) * (x2- x1) = F '(x1) (X2- x1) ?f (x2) - F (x1).

. (5.29). x1= X. f (x2) ?f (x) + f '(x) (x2- X). (5.30)

(5.30) x2 x1, f (x1) ?f (x) + f '(x) (x1-x). (5.31)

(5.30) t, (5.31) 1-t ,

tf (x2) + (1 - t) f (x1) ?f (x) + f '(x) (t (x2- x1) + X1-x).

x = x1+ T (x2- x1)

f (tx2+ (1 - t) x1) ?tf (x2) + (1 - t) f (x1), T ? [0; 1], . . (5.28).

f (x).

f (x) x1: Y = f (x1) + F '(x1) (X-x1).

(5.29) Y (x2) , , f (x2) ?Y (x2). 18 :

2. f (x) (a; b) , (x, f (x)), x? (a; b), f (x) (x1, F (x1)), X1? (a; b).



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