vv
vv

:

Internet Explorer 6 - v

Powered by Asuult.Net

(3- )

11- .

14

f, g [a, b] v (a, b)

g'(x)[f(b) - f(a)] = (x)[g(b) - g(a)]

(a, b) .

(g(x)=x 11- .)

h(x) = f(x)[g(b) - g(a)] - g(x)[f(b) - f(a)] . h(x) [a, b] v (a, b) . h(a) = f(a)g(b) - g(a)f(b) = h(b) 10- h'(x) = 0 - (a, b) .

0 = (x)[g(b) - g(a)] - g'(x)[f(b) - f(a)] .

:

15

. ,

.

(a-, a+) v :

  1. (x), g'(x) . ( v)
  2. g'(x)0 . ( v) (*)

f(a)=g(a)=0 f, g v . a < x < a+ 11, 14 - [a, x] . g(x)0 . , g(x)=0 11- g'(b)=0 b - (a, x) . (*) - . g(x)0 14- . 11-

g'(y)[f(x)-0] = (y)[g(x)-0]

- (, ) . -->a y-->a . (,) .

.

vv v 15- . . :)

v v. 2- . 2- , :

(, f(a)), (b, f(b)) f f .

f . vv v . . v v.

, f(x)

. , <x<b

.

16

f 㺺 ( f 2- ) f .

< b .

g''>0 ( g' ), g(a)=g(b)=f(a) . < x < b -

g(x) < g(a) = g(b)

. , g(x) > g(a) = g(b) (a, b) g(x1) - max 1 . max : g(x1)>g(a), g'(x1)=0. 11- [a, x1]

- 2 - .

g' . g(x)g(a)=g(b) . g(x)=g(a) v.

g(x)=g(a) g(x1)<g(a), < x1< x 1 . ( g(x) [a, x] .) 11- [x1, x] .

- 2 - .

g' .

g(x) < g(a) = g(b)

. , a<x<b

.

.

vvv (g''>0 -> g''<0) g'' . g''(x)=0 , vvv - . : g''(x)=0 v vv! - g'' 㺺 vv, v vv . ͺ㺺 (㺺) , v () - vv vv vv . v .

. (-, 0) ( -> ), (0, ) ( -> ) ? 2- ?

max, min, , v, v , , v. vv 人 ! ( ).

<-- (2) | vv | -->


?

:
e-mail:
v:
 


vv | vv | | | | | Links |

Copyright © 2003 . . .