sử dụng đạo hàm để tìm giá trị lớn nhất nhỏ nhất của hàm số - Pdf 24

SỬ DỤNG ĐẠO HÀM ĐỂ TÌM GIÁ TRỊ LỚN NHẤT, NHỎ NHẤT
CỦA HÀM SỐ
ITÓM TẮT LÍ THUYẾT


  
  
 
    
    
≤ ∀ ∈


∃ ∈ =


  
 
  

=

  
  
 
    
    
≥ ∀ ∈


∃ ∈ =

 
6
A / B
  
 
 

E1".'(01$%,"".;'F
++:$'."';&A/'B8%<60-+:
 !
"#$%&

'

'('

)*"+,&-./
"0*"'*

"'*

"'('*

"'*"
1"
( )
( ) ( )
( )
{ }
G H


  

= −

= ⇔ − − = ⇔

=

."(R=&A2P/PB
*2P)2PG*2G)PQ*K)S*P)GO
T:(
A P/PB
   PQ 

=
6
A P/PB
   PG 

= −

B*i 2
I9I;J:$K%"LLM"-

 H  = −
&
/
H H
π π

= − +


&
/
H H
π π
 

 
 
$ U"0"V+H)W
K
π
L

π
⇔ = ±
K K
  
H H H H L H L L H L
   
π π π π π π π π
       
− = = − − = − + = −
 ÷  ÷
 ÷  ÷
   
   
T:(()


[ ] [ ]
[ ]

H K GQ/G H/GQ
H K G/H
 

 

− ∈ − ∪

=

− + ∈


J."'

2GQG
K
H
HGQ


2Q 2 
(
GKH
G
P

( )
H H
  H H H G H K      = = + − + +
6?
H ≤
0

H
HH P H + +
6?
G K G K
H/ / H
H H

   
− − − +
∈ − ∪
   
   
")

H
P S− +
6?
G K G K
/
H H

 
− − − +

 

J."'


H−

G K
H
− −
Q
G K
H
− +

H
( )

 
2Q2 
"


P H K−
6'."'(R";"+
H
P H K/P H G
 
− +
 

   
⇔ ∆ ≥ ⇔ ≤ ≤ ⇔ ∈ − − ∪
   
\+]T2\
G H
H

 + =

H
G H
H
G GH
 P
GH
  

 
= − +
 ÷
 
0
( )
K K K
G H G H G H G H
K
  K 
H H

4        


G
P

0^+?>)
K K
P
^@>)
K K
P

B*i 6
I96I;

L L
P P
G  
G  
 

 
+ +
=
+ +
2
0
H
H
K
H  H

− −
= = = =
− −

M(
( )
( )
[ ]

H
S
Q Q/G
H S
4 5 5
5

= < ∀ ∈

^_"'&AQ/GB0
I9;^_)^Q)GI9;^_)^G)
O
L
B*i 7
$ U"
H H
H H G P K Q    + + + + + =
I[
G

H

H G S X S X
H H H
 
6     
+ +
= + + = + + = − + +
&A2O/2GB
0

P6 = − −
&A2O/2GBJ."'
 2O2P2G

6
Q2
a

N
H

PQ
T:(I9;a'b"
N
H
789#:;<':<<)=>
B*i 8 

H H
G + =
;

H G
K H G
K H G



?
 
 
 
 
+
 ÷
+
 
= =
+ +
 
+ +
 ÷
 
6?



=
0
( )
H


+ +
J."'
 23
G

H
3

?
2QQ2
M
Q
H L
H
+

H L
H


Q
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