y = f (x) [ a, b ] (. 3.6).
. 3.6.
. h > 0. f (x 1) f (x 2) 1 = 2 = 1 + h. . . 3 = 2 + h f (x 3). f (x 3). . , b. .
. , . 3.6, , . . . . , , ( ) .
. f (x) [ a, b ], , .
, [ a, b ] , . . .
, , 1 2 , < 1 < 2 < b. (. 3.7). min [ x 2, b ], [ a, x 1] ( ). , , 3 : [ a, x 2] 1 [ x 1, b ] 2.
, [ a, b ] 1 2. min , . , : [ x 2, b ] [ a, x 1]. , 1 2 [ a, b ].
. 3.7.
, , . , .
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, , , , , . .
[ a, b ] [0, 1] (. 3.8).
. 3.8.
. 3.8 ÷ ê=÷ CD ê= , ÷ C ê=÷ D ê= 1 , ÷ ê= 1 2 .
, B , (), AD , AC: AB / AD = BC / AC. C: CD / AD = BC / BD. x : x /1 = (1 2 x)/(1 x). :
(1 ) = 1 2 Þ 2 = 1 2 Þ 2 1 + 2 = 0 Þ 2 + 3 1 = 0 Þ 2 3 + 1 = 0; = b 2 4 ac = 9 4 = 5.
:
.
x 2 > 1 , . . .
, , , . , , .
, (. 3.9). [ a, b ] x 1 x 2, , . f (x 1) f (x 2). , , , ( [ x 2, b ]). . . [ a, b ] [ a, b 1].
. 3.9.
, x 1 x 3. f (x 3) f (x 1). , , [ a, x 3]. , [ a 1, b 1] . .
, .
, . , .
1. 2 , . : 1 2. = 2 / 1 max, :
1 £ 1 £ 8, 2 £ 2 £ 12, 1 × 2 ³ 10.
. :
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lg 1 £ lg 1 £ lg 8; lg 2 £ lg 2 £ lg 12; lg 1 + lg 2 ³ lg 10.
:
0 £ lg 1 £ 0,903; 0,301 £ lg 2 £ 1,079; lg 1 + lg 2 ³ 1.
:
lg y = lg 2 lg max.
- -.
2. (, ) .
Q :
Q = B × n × S max,
B ; n ; S .
. , :
Q = n × S max.
, . . . . :
ln Q = ln n + ln S. Z = ln Q;
x 1 = ln n; x 2 = ln S; Z = x 1 + x 2 max.
, S min, S max, n min, n max, , , . - . 3.10.
. 3.10.