







 !"#$%
Dng 1
a vào  th hàm s
( ) : ( )=C y f x
&'( th hàm s
1 1
( ) : ( )=C y f x
)*+,
1 1
0
( ) : 0
≥
= = − ≤
y y
C y y y y


*-*+-*./01
1 1
( ) : ( )=C y f x
)*+20.-*./01,
30.,450.-*./01
( ) : ( )=C y f x
6708/9
30.2,450.-*./01
( ) : ( )=C y f x
6708:;<+9
4=(-*=9;+>'9
Dng 2
a vào  th hàm s
( ) : ( )=C y f x
&'( th hàm s
2 2
( ) : ( )=C y f x
09+/,
2 2
( ) : ( )=C y f x
45057&*=)0?

2 2
( ) : ( )=C y f x
0(457/'@)-*=9;+A
)*+,
2 2
( ) 0 (1)
( ) : ( ) ( ) 0
= ≥
= = − ≤
f x y
C y f x f x


*-*+-*./01 2 2
( ) : ( )=C y f x
)*+20.-*./01,
30.,450.-*./01
( ) : ( )=C y f x
6708B0C(

30.2,450.-*./014=(-*=9;+>'(DE057&*=)0?
Dng 3
a vào  th hàm s
( ) : ( )=C y f x
&'( th hàm s
3 3
( ) : ( )=C y f x
09+/,='
0 0 3 0 0 3
( ; ) ( ) ( ; ) ( )∈− ∈
M x y C M x y C


3 3
( ) : ( )=C y f x
09457/'@)-*=9;+A
)*+, 3 3 3
( ) : ( ) 0= = = ≥C y f x y y y y
Traàn Phuù Vöông





2

*-*+-*./01
3 3
( ) : ( )=C y f x
)*+20.-*./01,
30.,450.-*./01
( ) : ( )=C y f x
6708/9
30.2,450.-*./014=(-*=9;+>'9A
Dng 4
a vào  th hàm s
( ) : ( ) ( ). ( )= =C y f x u x v x
&'(
th hàm s
4 4
( ) : ( ) . ( )=C y u x v x
)*+,
4 4
( ). ( ) ( ) ( ) 0
( ) : ( ) . ( ) ( ). ( ) ( ) ( ) 0
= = ≥
= = − = − = − ≤
u x v x f x y u x
C y u x v x u x v x f x y u x


*-*+-*./01
4 4
( ) : ( ) . ( )=C y u x v x
)*+20.-*./01,
30.,450.-*./01
( ) : ( )=C y f x
67/7.
( ) 0≥u x
30.2,450.-*./01
( ) : ( )=C y f x
67/7.
( ) 0≤u x
4=(-*=9;+>'9

a vào  th hàm s
( ) : ( ) ( ). ( )= = −C y f x x a v x

&'( th hàm s
4 4
( ) : . ( ),= − ∈ C y x a v x a
)*+,
4 4
( ). ( ) ( )
( ) : . ( ) ( ). ( ) ( )
− = = ≥
= − = − − = − = − ≤
x a v x f x y x a
C y x a v x x a v x f x y x a


*-*+-*./01
4 4
( ) : . ( ),= − ∈ C y x a v x a

)*+20.-*./01,
30.,
450.-*./01
( ) : ( )=C y f x
67B0C-;<5/0F9G
30.2,450.-*./01
( ) : ( )=C y f x
67B/+
-;<5/0F9G4=(-*=9;+>'9A
Traàn Phuù Vöông





H


;5I:@-*./01)*+)0;+:='+/1/'(/-*=)<BC//)*+/0J&'(
0.':@-*./01)*+)0;+:='+/1/'(/-*=K0+))0F0@,
Dng 5
a vào  th hàm s
( ) : ( )=C y f x
&'( th hàm s
5 5
( ) : ( )=C y f x
%JDL
5 5
( ) : ( )=C y f x
/4572B;<+)0;&',
3M;<+),DL
51
( ) ( )= =y f x g x
:;@D5*:@2
3M;<+)2,DL
5
( ) ( )= =y f x g x
:;@D5*:@
Dng 6
a vào  th hàm s
( ) : ( )=C y f x
&'( th hàm s
6 6
( ) : ( )=C y f x
%JDL 6 6
( ) : ( )=C y f x
/4572B;<+)0;&',
3M;<+),DL
61
( ) ( )= =y f x g x
:;@D5*:@2
3M;<+)2,DL
6
( )=y g x
:;@D5*:@H
Dng 7
a vào  th hàm s
( ) : ( )=C y f x
&'( th hàm s
7 7
( ) : ( )=C y f x
%JDL
7 7
( ) : ( )=C y f x
/457HB;<+)0;&',
3M;<+),DL 71
( ) ( )= =y f x g x
:;@D5*:@2
3M;<+)2,DL
72
( ) ( ) ( )= = =y f x g x h x
:;@D5*:@
3M;<+)H,DL 7 7
( ) : ( )=C y h x
:;@D5*:@H
Traàn Phuù Vöông





I

$NOPP

0*057&*=
3 2
2 3 1y x x= − +
)*+-*./01QRA
0C*&+/D5DL-*./01QR)'C057&*=A

N=/0;</E0/=/'(=)'C-*./01QR/@*-J7)'CQR
D<+-;<5/0F9G
−
A
HRE7/07&*=7-J0;</E0
32
2 3 2x x m− + =
)*+B*=
070B/A

C
0C*&+/D5DL-*./01QR)'C057&*=A

2
' 6 6y x x= −

' 0 0y x= ⇔ =

1x=

−∞ 
+∞

 !"#$ %$#$&$&
0; 1x y= =

 !"#$%$& '$&
1; 0x y= =

lim
x
y
→±∞
= ±∞



−∞
S
+∞

T
3SUS3

+∞


−∞


'' 12 6y x= −

'' 0y x= ⇔ =
()

−∞

+∞
TUS3
V*.%V*L7
QW2XW2R


N=/)'C-*./01QR/@*-J7)'CQRD<+-;<5/0F9G
−
9G
−
GY(GZQ
−
RG
−
IGY*-J7Q
−
X
−
IR
///)*+:@
,000
)).((' yxxxfy +−=
A
0
'( ) '( 1) 12f x f= − =
GY///
,
12( 1) 4 12 8y x x= + − = +
A
-5 -4 -3 -2 -1 1 2 3 4 5
-5
-4
-3
-2
-1
1
2
3
4
5
x
y
P
Q
O

* −−+
,)-
3 2
2 3 1y x x= − +
./0
#&'!12 !
!#&%3
4
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




[

E7/07&*=7-J0;</E0 32
2 3 2x x m− + =
)*+B*=07
0B/A
)*+, 3 3
2 2
2 3 2 2 3 1 1x x m x x m− + = ⇔ − + = −
%(45%%)'C-*./01
1
( )C
,32
1
2 3 1y x x= − +
D5-;<5/0F
:,(G7
−

)*+
1
( )C
,
3 2
13 2
2 3 1 0
2 3 1 0
x x x
yx x x
− + ≥
=− − + <



GY
1
( )C
)*+20.-*./01,
0.,%*./01QR67B0C/'@)(Q)C-J767/(R
0.,V=(-*=9;+-*./010.>'(
DE057&*=
1
y
45057&*=)0?
NL
1
( )C
Q
E02R
-5 -4 -3 -2 -1 1 2 3 4 5
-5
-4
-3
-2
-1
1
2
3
4
5
x
y
Q
O
32
1
2 3 1y x x= − +
4)

;@D5*
1
( )C
/)*+,S\7
−
\\GY\7\2

0*057&*=
4 2
14 3
2
y x x= − +
)*+-*./0145

0C*&+/D5DL-*./01)'C057&*=A
Traàn Phuù Vöông