Embed Size (px)
Citation preview
48
öflÎI�������Âflbr€a@ÖÜ»€a����������H@pb
49
öflÎI�������Âflbr€a@ÖÜ»€a����������H@pb
2( )f x ax bx c= + +
0a ¹a
( )
( )( )
2 2
2
2 2
2 2
1( ) 4 4 4
4
12 2 (2 ) 4
4
1(2 ) 4
4
1(2 ) ( 4 )
4
f x a x bax aca
ax b ax aca
ax b b aca
ax b b aca
= + +
= + +
é ù= + - +ë û
é ù= + - -ë û
2 4b ac= -2b2 4= bb
21( ) (2 )
4 4f x ax b
a a= + -
0a >( )f x2 0ax b+ =2
2
bx
a= -x
4a--
,2 4
b
a a
æ ö- -ç ÷è ø
ö÷ööæ
çææ
èçç
0a <( )f x2 0ax b+ =2
2
bx
a= -
4a--,
2 4
b
a a
æ ö- -ç ÷è ø
ö÷ööæ
çææ
èçç
,2 4
b
a a
æ ö- -ç ÷è ø
ö÷ööæ
çææ
èçç
).هو مشتقة الدالة( لاحظ أن
50
öflÎI�������Âflbr€a@ÖÜ»€a����������H@pb
2 2( , )f x y ax bxy cy dx ey k= + + + + +f
0a¹0b¹0c¹c0b¹b
2 2 2
2 2 2 2
2 2
1( , ) (4 4 4 )
4
1(2 ) 4
4
1(2 ) 4 4
4
f x y a x abxy acy dx ey ka
ax by b y acy dx ey ka
ax by adx aey y ka
= + + + + +
é ù= + - + + + +ë û
é ù= + + + - +ë û kù2 22 2
ûyyyyyy2 2yyy2 22 2
II0¹0¹
2 2
2 2 2
22 2
22 2 2
1( , ) (2 ) 2 (2 ) (4 2 )
4
1(2 ) (4 2 )
4
1 2(2 ) 2
4
1 2 2(2 ) ( ) ( )
4 4
f x y ax by d ax by ae bd y y ka
ax by d d ae bd y y ka
ae bd dax by d y y k
a
ae bd ae bd dax by d y k
a a
é ù= + + + + - - +ë û
é ù= + + - + - - +ë û
é ùæ ö-æ ö= + + - - + +ê úç ÷ç ÷è øè øë û
é ù- -= + + - - - + +ê ú
ë û
kù2 22 2
ûyyyyyy2 2yyyy2 22 2
kù2 2 22 2 2
ûyyyyyy2 2 2yyy2 2 22 2 2
2 22 22 22 22 22 22 22 22 22 22 22 22 22 22 2 222 22 2 22 22 22 22 22 22 22 22 22 22 22 2 222 22 22 2
èçç yyyy
èçç kyyyy
ûúúø÷÷y
ø÷÷
2 2 22 2 22 2 22 2 2é 22 2 22 2 22 2 2222 2 22 2 22 2 22 2 22 2 22 2 22 2 22 2 22 2 22 2 22 2 22 2 22 2 22 2 22 2 22 2 22 2 22 2 22 2 22 2 22 2 22 2 22 2 22 2 22 2 22 2 22 2 22 2 22 2 22 2 22 2 22 2 2((((2 2 22 2 22 2 22 2 2 k) ( )) ( )) ()ûúú) ( )
0
2ae bdy
-=
2 22 2
0
1 (2 )( , ) (2 ) ( )
4 4 4 4
ae bd df x y ax by d y y k
a a a a
-= + + - - + - +2 22 22 22 2( )( )( )0
2 22 22 2
44a a4
yyyxaac
ddee0c¹c
2 22 2
0
1 (2 )( , ) (2 ) ( )
4 4 4 4
cd be ef x y cy bx e x x k
c c c c
-= + + - - + - +2 22 22 22 22 2( )( )( )0
2 22 22 2
44c c4
0
2cd bex
-=x2 4b ac= -2b a2 4= bb
حيث أن
51
öflÎI�������Âflbr€a@ÖÜ»€a����������H@pb
0
2
2
2
d b
e cx
a b
b c
-
-=x0
2
2
2
a d
b ey
a b
b c
-
-=
0 0( , )x y
2 0
2 0
ax by d
bx cy e
+ + =ìí
+ + =î
2 2
0 0
(2 )( , )
4 4
ae bd df x y k
a a
-= - +
44a a4
2 2
0 0
(2 )( , )
4 4
cd be ef x y k
c c
-= - +
44c c4
2 2
0 0 0
1( , ) (2 ) ( ) ( , )
4 4f x y ax by d y y f x y
a a= + + - - +2 22 22 22 2( )( )( )2 22 22 2
0 0 00 0 0
2 2
0 0 0
1( , ) (2 ) ( ) ( , )
4 4f x y cy bx e x x f x y
c c= + + - - +2 22 22 2( )2 22 22 2
0 0 00 0 0
0 0( , )x y(
2 0
2 0
ax by d
cy bx e
+ + =ìí
+ + =î
2 2 2 2
0 0 0 0
1 1( , ) (2 ) ( ) (2 ) ( ) ( , )
8 8f x y ax by d y y cy bx e x x f x y
a cé ù é ù= + + - - + + + - - +ë û ë û0 0 0 0
1)0f0 0 00 0 0((0 0 00 0 00 0 0
c8é ù2 2 2 22 2 2112 2 22 2 22 2 22 2 2 22 2 22 2 22 2 22 2 22 2 22 2 2 22 2 22 2 22 2 22 2 22 2 22 2 22 2 2
0 0 00 0 0ë û0 0 00 0 088
0 0 00 0 00 0 00 0 00 0 00 0 0(( 0 0 00 0 00 0 00 0 00 0 00 0 00 0 0(( 0 0 00 0 00 0 00 0 0c88
(( 0 0 00 0 00 0 00 0 00 0 00 0 0
2 2 2 22 2 22 2 22 2 22 2 22 2 2( ) (2 ) ( )( ) (2 ) ( )( ) (2 ) ( )( ) (2 ) ( )( ) (2 ) ( )( ) (2 ) ( )2 2 2 22 2 22 2 22 2 22 2 22 2 2
0 0 00 0 00 0 00 0 00 0 00 0 0
52
öflÎI�������Âflbr€a@ÖÜ»€a����������H@pbIII0D =
2
2
2 2
22
1( , ) (2 ) 4 4
4
1(2 ) 2 (2 ) 2 4
4
1(2 ) 2(2 )
4
1 1(2 ) (2 )
4 2 4
f x y ax by adx aey ka
ax by d ax by bdy aey ka
ax by d d ae bd y ka
dax by d ae bd y k
a a a
é ù= + + + +ë û
é ù= + + + - + +ë û
é ù= + + - + - +ë û
= + + + - + -
( , )f x yf
2 2
0 0 0
1( , ) (2 ) ( ) ( , )
4 4f x y ax by d y y f x y
a a
D= + + - - +
0<0<0a>a0 0( , ) ( , )f x y f x y³f( , )x y(
0 0( , )x y
0D <D0a<a0 0( , ) ( , )f x y f x y£
0 0( , )x y
0D>D0a>
( , )x y(2 0ax by d+ + =
2
0 0 0( , ) ( ) ( , )4
f x y y y f x ya
D=- - +f-¥-y¥
2
0 0 0 0
1( , ) (2 ) ( , )
4f x y ax by d f x y
a= + + +f¥¥x¥
0D>D0a<a
53
öflÎI�������Âflbr€a@ÖÜ»€a����������H@pb
IIII0D=
2 0ae bd- =22
221
( , ) (2 )4 4
df x y ax by d k
a a= + + + -
0a>a
2 0ax by d+ + =2
4
dk
a-k
0a<
2 0ax by d+ + =2
4
dk
a-k
0D=D2 0ae bd- =2
2 0
2 0
ax by d
bx cy e
+ + =ìí
+ + =î
2 0ax by d+ + =2
0=0=2 0ae bd- ¹
221 1
( , ) (2 ) (2 )4 2 4
df x y ax by d ae bd y k
a a a= + + + - + -
1 1( , )x y1 12ax by d h+ + =
22
1 1 1
1 1( , ) (2 )
4 2 4
df x y h ae bd y k
a a a= + - + -
:للهيئة أن هو الشرط معنى
.متناقضتان لمعادلتانا: القول يكافئ وهو .لا يوجد حل
54
öflÎI�������Âflbr€a@ÖÜ»€a����������H@pb 2ax by d h+ + =
1 1( , )x y(
( ', ')f x yf( '', '')f x y
1 1( , )f x yf1 1( , )f x y
1 1( , )f x yf
2 0
2 0
ax by d
bx cy e
+ + =ìí
+ + =î
( , )f x yfyx
( , )f x yf
( , )f x yfyy
55
öflÎI�������Âflbr€a@ÖÜ»€a����������H@pb2 2( , ) 4 7 5 4 12f x y x xy y x y= + + - +
27 4 4 5 31 0D = - × × = - <D4 0a = >a
8 7 4 0
7 10 12 0
x y
x y
+ - =ìí
+ + =î
0 0( , ) (4, 4)x y = -
min (4, 4) 32f f= - = -
2 2
2 2 2
2 2
2 2
2 2
2
1( , ) (16 28 20 ) 4 12
4
1 7 7(4 ) ( ) 20 4 12
4 2 2
1 7 31(4 ) 4 12
4 2 4
1 7 31(4 ) 16 48
4 2 16
1 7 7 31(4 ) 4(4 ) 62
4 2 2 16
1 7 7(4 ) 4(4 )
4 2 2
f x y x xy y x y
x y y y x y
x y y x y
x y x y y
x y x y y y
x y x y
= + + - +
é ù= + - + - +ê úë û
é ù= + + - +ê úë û
é ù= + - + +ê úë û
é ù= + - + + +ê úë û
é ù= + - +ê úë û2
2 2
2 2
2 2
31 31
16 2
1 7 31(4 2) 4 ( 8 )
4 2 16
1 7 31(4 2) ( 4) 31 14 2 16
1 31(8 7 4) ( 4) 32
16 16
y y
x y y y
x y y
x y y
+ +
é ù= + - - + +ê úë û
= + - + + - -
= + - + + -
0 4y = - 0 4x =x
56
öflÎI�������Âflbr€a@ÖÜ»€a����������H@pb
2 2( , ) 6 9 8 12f x y x xy y x y= + + - -
26 4 1 0 0D = - × × =
2 2 1 ( 12) 6 ( 8) 24 0ae bd- = × × - - × - = ¹
2
2
2
( , ) ( 3 ) 8( 3 ) 12
( 3 4) 12 16
(4 3 , ) 0 12 16
f x y x y x y y
x y y
f y y y
= + - + +
= + - + -
- = + -
yy¥¥¥
y-¥-¥-
1 1( , )x y1 13 4x y h+ - =
2 2( , )x y3 3( , )x y1 1( , )x y1 1( , )x y(
2 2 2( , ) 12 16f x y y= -f3 3 3( , ) 12 16f x y y= -
2 1 3y y y> >y2 2 1 1 3 3( , ) ( , ) ( , )f x y f x y f x y> >
1 1( , )x y
57
öflÎI�������Âflbr€a@ÖÜ»€a����������H@pb
2 2( , )f x y ax bxy cy dx ey k= + + + + +
2 4b acD = -D
2 0
2 0
ax by d
bx cy e
+ + =ìí
+ + =î
0D <0a <0 0( , )x y(
2 0
2 0
ax by d
bx cy e
+ + =ìí
+ + =î
0D <D0a >0 0( , )x y(
2 0
2 0
ax by d
bx cy e
+ + =ìí
+ + =î
0D >D
0D =2 0ae bd- ¹2
0D =2 0ae bd- =20a <
2 0ax by d+ + =22
4
dk
a-k
0a >2 0ax by d+ + =2
2
4
dk
a-k
58
öflÎI�������Âflbr€a@ÖÜ»€a����������H@pb
2 2( , )f x y ax cy dx ey k= + + + +
ü ,2 2
d e
a c
æ ö- -ç ÷è ø
ü ,2 2
d e
a c
æ ö- -ç ÷è ø
æçææ
èçç
ü
ü
![[XLS]syamsulhadiblog.files.wordpress.com · Web view15 0 25 0 1 0 1 0 40 0 35 0 1 0 1 0 50 0 50 0 2 0 2 0 50 0 65 0 2 0 2 0 110 0 110 0 2 0 2 0 85 0 60 0 3 0 2 0 60 0 55 0 2 0 2 0](https://img.pdfslide.tips/doc/110x75/5ba0961809d3f2df578d21b0/xls-web-view15-0-25-0-1-0-1-0-40-0-35-0-1-0-1-0-50-0-50-0-2-0-2-0-50-0-65.jpg)
