!"#$
( )
1 2
1 2
2
1 2
1 2
2 max
2 2 1
0
2 1
4 3
f x x x
x x
x
x x
x x
= + ®
ì
ï
- £ -
ï
ï
ï
£
ï
ï
í
ï
+ £ -
ï
ï
ï
- + £
ï
ï
î
%&&#&''&(
( ) ( )
1 2 3 4
2 1 7 1
1,0 , , , 7, 1 , ,
3 6 9 9
x x x x
æ ö æ ö
÷ ÷
ç ç
÷ ÷
= - = - - = - - = - -
ç ç
÷ ÷
ç ç
÷ ÷
ç ç
è ø è ø
2. )&*$+,)&-)&
. /01)&*2&'&#
a)
( )
3 .
4 5
3 4 6 5
. 4 6 5
3 6
3 . .
3 6 5 6
7 5
= + + →
− − =
+ − + =
+ − + =
≥ ∀ =
j
f x x x x
x x x
x x x x
x x x x
x j
b)
8
9
!"
%:
#
( )
= + + ®
ì
ï
+ + =
ï
ï
ï
- + =
í
ï
ï
³ =
ï
ï
î
1 2 3
1 2 3
1 2 3
1) 3 2 max
1
1
0, 1,2,3
j
f x x x x
x x x
x x x
x j
( )
1 2 3
1 2 3
1 2 3
1 2 3
2) min
1
1
1
f x x x x
x x x
x x x
x x x
= + + ®
ì
ï
- + + £
ï
ï
ï
- - - £
í
ï
ï
- - + £
ï
ï
î
3 )&*$+-)&&(;)&
3. <'';=>?@%9
?
A
B1;=>?
@
4 /01)&*2&'&#
( )
3 . 4 6
3 . 4 6
3 . 4 6
3 . 4 6
3 5 6 4
4 3 6 C .
. 4 6 5
7 6
j
f x x x x x x Min
x x x x x
x x x x
x x x x
x j
= + - + + ®
ì
- + - + =
ï
ï
ï
ï
- + - =
ï
ï
í
- + - =
ï
ï
ï
ï
³ =
ï
ï
î
Đ ́
( )
3 .
3 .
3 .
3 .
.
3 4
3 3
. 3
. 4 .
7
f x x x x Max
x x x
x x x
x x x
x
= + - ®
ì
+ - £
ï
ï
ï
ï
+ + £ -
ï
ï
í
ï
+ - £
ï
ï
ï
³
ï
ï
î
!"#$%&'(&)*+( &)&Đ ́ ươ
III.
#
#?
DE%F&
( )
1,2,0,0,0x =
'&(#?<G,'&
( )
2 3 4 5
1 2 3 5
1 2 4 5
1 2 3 4
2 2 2 max
2 3 4
4 5 3 6
2 2 3
0, 1,5
j
f x x x x x
x x x x
x x x x
x x x x
x j
= + - - ®
ì
ï
- + + + =
ï
ï
ï
- + - = -
ï
ï
í
- + + - =
ï
ï
ï
ï
³ =
ï
ï
î
3 )&&<$+-)&
. H#&3)&$'&<
4 /01)&&<2&'&#
a)
( )
3 .
3 .
3 .
3 .
4 6 3
5
3 .
3 7
7 .
j
f x x x x Min
x x x
x x x
x x x
x j
= + - ®
ì
+ + £
ï
ï
ï
ï
+ - =
ï
ï
í
+ - =
ï
ï
ï
ï
³ =
ï
ï
î
I
#
$>JKL73M
b)
( )
3 .
3 .
3 .
3 .
3 3
4 3
3 4 4
7 .
j
f x x x x Min
x x x
x x x
x x x
x j
= + - ®
ì
- + =
ï
ï
ï
ï
- + =
ï
ï
í
+ - ³
ï
ï
ï
ï
³ =
ï
ï
î
I
#
$N
1. N
A
O:
A
2. )&9
A$+-)&
.
a) 9
A
#?P
:
9
A
#?%
O
A
( )
3 .
3 . 4
3 . 6
3 . 5
. 3
4 6 Q R
3 4 3 3
. 3 3
7 5
= + + →
− + + =
− + − + = −
− + + =
≥ =
j
f x x x x
x x x x
x x x x
x x x x
x j
b)
{ }
.46=J
#
A
#?:
9
A
( )
3
3 . 4
3 4
3 4 6
3 3 .
.
3
7 6
= + →
− + + = −
− + =
− + + =
≥ ∀ =
j
f x x x
x x x x
x x x
x x x
x j
1.
?
A?
9
A
?
?
9
0
3
"
3. "
>?
%9
?
A
:
>?
4. P
#
( )
3 .
3 .
3 .
3 .
3
3
3 3
6
3 3
7 .
= − − →
+ − ≤
− + ≤
+ ≤
− ≤
≥ ∀ =
j
f x x x x
x x x
x x x
x x
x x
x j
%9
??
9
A
A
?
?
?
9
A
9
0
3
( )
3 . 4 6
3 . 4 6
. 4 6
3 . 6
6 C 6 Q .
3 5 3 3 4
R 3 4 37
7 36
= − + + + →
+ − − + ≤ −
+ + − =
− − + − ≥ −
≥ =
j
f x x x x x x
x x x x x
x x x x
x x x x
x j
%:
( )
7767=x
A
9
A
. 9
A
#?P
:
9
A
#?%
O
A
( )
3 .
3 .
3
3 .
4 Q .
3 4
3 4
3 3 .
7 .
= + + →
− + − ≤
+ ≥
− + ≤ −
≥ =
j
f x x x x
x x x
x x
x x x
x j
!
!
"
#
$
8
9
!"
%:
#
( )
= - ®
ì
ï
+ £
ï
ï
ï
+ £
ï
ï
í
ï
+ ³
ï
ï
ï
³ ³
ï
ï
î
1 2
1 2
1 2
1 2
1 2
1) 3 min
2 5 10
2 6
2 2
0, 0
f x x x
x x
x x
x x
x x
( )
= + + ®
ì
ï
+ + ³
ï
ï
ï
- - =
ï
ï
ï
ï
- - £
í
ï
ï
+ £
ï
ï
ï
ï
+ ³
ï
ï
î
1 2 3
1 2 3
1 2 3
1 2 3
1 3
2 3
2) 3 7 min
6
3 2 14
4 5 12
4 10
2 7
f x x x x
x x x
x x x
x x x
x x
x x
3
>?
%9
?
:
>?
9
0
. ST
A
9
#
0
4 P
!"#?
( )
3 . 4 6
3 4 6
3 . 4 6
3 6
3 6 4 6
5 3 C .3
3 U 3 . U 6 .7
. .5
7 6
j
f x x x x x x Min
x x x x
x x x x
x x
x j
= + + + - ®
ì
- - - =
ï
ï
ï
ï
+ + + =
ï
ï
í
+ £
ï
ï
ï
ï
³ =
ï
ï
î
I
#
$>JKL.37.777MVL>JMKR4
!
!
"
#
$
1.
D%FGWX'&#
x
'&G
$
( )
( )
= + ®
ì
ï
- + + + =
ï
ï
ï
- + + + =
ï
ï
í
ï
+ =
ï
ï
ï
³
ï
ï
î
= -
2 4
1 2 3 4
1 2 3 4
2 4
1
) min
2 1
2 2
3 2 3
0
0, 1,0,3
a f x x x
x x x x
x x x x
x x
x
x
( )
( )
= + ®
ì
ï
+ + + =
ï
ï
ï
+ + + £
ï
ï
í
ï
- + + + =
ï
ï
ï
³
ï
ï
î
= -
1 4
1 2 3 4
1 2 3 4
1 2 3 4
1
) max
1
3 2 4
9 4 16
0
0,1,3, 3
b f x x x
x x x x
x x x x
x x x x
x
x
3 %9
?
9
T
A
9
?
9
0
%
0?
#
:
9
. %9
?
!":
9
:
9
AY
:
A
4 P
!"#:
9
A
( )
3 . 4 6
3 . 4 6
3 . 4 6
3 . 4 6
3 5 6 4
4 3 6 C .
. 4 6 5
7 6
j
f x x x x x x Min
x x x x x
x x x x
x x x x
x j
= + - + + ®
ì
- + - + =
ï
ï
ï
ï
- + - =
ï
ï
í
- + - =
ï
ï
ï
ï
³ =
ï
ï
î
Yêu cầu:
Z
:
0
Z [A
$"
Z
0
:
H0T#
Z
%9
?
0
Z %