Bài tập giải tích cổ điển cực trị hàm số ôn thi cao học

Bài tập giải tích cổ điển luyện thi cao học Đại Học Cần Thơ

Người soạn: Nguyễn Anh Quốc Trang 1

CC TR 








































m M(x
0
;y
0
c gm cc
tiu(c f(x;y). Cc tii gc tr 
C TR N S
C I

















C II:





































 




























 

 

 


Gii





 

 



  












 

 
  



 

 





























  





  






  t cc tr ti 







  t cc tr ti 







  t cc tiu ti 







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
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

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

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














Gii





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





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
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
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



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



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




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
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

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



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





 

m nghi ng c tr
Ta thm M
1
m (x;y
0

0
)- z(0;y
0
) = x
3
y
0
3
m (x;y
0

z(x;y
0
)- z(0;y

0
) = x
3
y
0
3
< 0












 








 cho M
2

Bài tập giải tích cổ điển luyện thi cao học Đại Học Cần Thơ

Người soạn: Nguyễn Anh Quốc Trang 2







Gii












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
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
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




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







































 

m nghi ng c tr






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
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








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



P
c tr c y Nguyn H
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 

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


 
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 



Gii

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
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
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

  
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








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





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





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  t ci t-2;2) = 8
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



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

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
t
0 1 

+ 0 -
z




0 0
Bài tập giải tích cổ điển luyện thi cao học Đại Học Cần Thơ

Người soạn: Nguyễn Anh Quốc Trang 3


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


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










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

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

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
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n tm dng



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
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 
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 
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 n tp mi (0 ;0)






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








Bài tập giải tích cổ điển luyện thi cao học Đại Học Cần Thơ

Người soạn: Nguyễn Anh Quốc Trang 4

c tr c s sau


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Bài tập giải tích cổ điển luyện thi cao học Đại Học Cần Thơ

Người soạn: Nguyễn Anh Quốc Trang 5

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Bài tập giải tích cổ điển luyện thi cao học Đại Học Cần Thơ

Người soạn: Nguyễn Anh Quốc Trang 6

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Bài tập giải tích cổ điển luyện thi cao học Đại Học Cần Thơ

Người soạn: Nguyễn Anh Quốc Trang 7

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Bài tập giải tích cổ điển luyện thi cao học Đại Học Cần Thơ

Người soạn: Nguyễn Anh Quốc Trang 8

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  
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 thi th



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
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 
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 
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       
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



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

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 



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Gii


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

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   
c tr c

  
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 
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   t v(x ;y)=

 
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    
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  
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
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










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  


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    
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


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













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






Bài tập giải tích cổ điển luyện thi cao học Đại Học Cần Thơ

Người soạn: Nguyễn Anh Quốc Trang 9



 
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

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
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
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
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

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
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
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
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 
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     





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
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Bài tập giải tích cổ điển luyện thi cao học Đại Học Cần Thơ

Người soạn: Nguyễn Anh Quốc Trang 10


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
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



Bài tập giải tích cổ điển luyện thi cao học Đại Học Cần Thơ

Người soạn: Nguyễn Anh Quốc Trang 11

CC TR U KIN
 : Cc tr c z = f(x,y) vu kic 




 c gc tr 
u kin.
I
1. 
T u kic 



 ta gic tr u kin c
s z = f(x,y) c quy v vic tr t u kin) c
z = f(x,y(x))


  
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 

   
Gii :
      


  



  





 










  
  







x
0


1

+ 0 -
z





0 1













2.  Lagrange








 














































 









  
















  




 
































































    

 


Gii




     




 

 
















  
  


 

 









































  




  

 

  











  
















 




 


















 




 









 



 


Bài tập giải tích cổ điển luyện thi cao học Đại Học Cần Thơ

Người soạn: Nguyễn Anh Quốc Trang 12










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






 































 















    
Gii




     






















  
  
  
  

































 




  




  





    









    






    




   
















 










p
m cc tr u kiy Nguyn H


 




























    









Gii


 












  




  





  




















































 




























































































Bài tập giải tích cổ điển luyện thi cao học Đại Học Cần Thơ

Người soạn: Nguyễn Anh Quốc Trang 13








































 











 


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
 










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
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

 



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





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
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


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





 





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
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
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
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


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





 


























    














      







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 





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

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
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
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 

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









 















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


























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
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  
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  
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
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
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
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
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
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

 


 






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
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
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


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


 

 








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 

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 


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



   














 i.









Bài tập giải tích cổ điển luyện thi cao học Đại Học Cần Thơ

Người soạn: Nguyễn Anh Quốc Trang 14



c tr u kin c sau
  


 

 






















    


 

 









    

Gii
  
T u ki u thc z = x(1  x) = x  x
2



  





















 

 













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









 

 
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 



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
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
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

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
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 




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
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



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
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

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 
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
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
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 
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 
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 
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
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
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
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 
















































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





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
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
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 

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
  




  





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

Bài tập giải tích cổ điển luyện thi cao học Đại Học Cần Thơ

Người soạn: Nguyễn Anh Quốc Trang 15

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     


Bài tập giải tích cổ điển luyện thi cao học Đại Học Cần Thơ

Người soạn: Nguyễn Anh Quốc Trang 16


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Bài tập giải tích cổ điển luyện thi cao học Đại Học Cần Thơ

Người soạn: Nguyễn Anh Quốc Trang 17


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



Bài tập giải tích cổ điển luyện thi cao học Đại Học Cần Thơ

Người soạn: Nguyễn Anh Quốc Trang 18

 NH NH LN NHT

Nh u bi chn D s t mt l nh nh
ln nh nh nh ln nht ti mm trong mi
m cc tr c nh nh ln nht c
t nh ca D.
i tr nh nh ln nh chn
  nh nh ln nht ca m chn D trong mt phng ta
m cc tr c phn trong ca D. N
c
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tr vu kin 
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  cc .
S nh nht, ln nhng s  nh nht, ln nht cn D.
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

 








 

 







 

   



 

 


4
3
2
1
-1
-2
-3
-8
-6
-4
-2
2
4
6
8
10
B
A

O
Bài tập giải tích cổ điển luyện thi cao học Đại Học Cần Thơ

Người soạn: Nguyễn Anh Quốc Trang 19















   
   


 

 


































p

 nh nhy Nguyn H
  

 




 



 






    

  
    

  










Gii
  

 


m ti hn thuc min trong c nht OABC



  




Gii h 











  


















































  





























  











  



























  


 








  




































 



 


m ti hn trong min 

 











Gii h 
4
2
-2
-4
-10
-5
5
10
C
B
A
O
Bài tập giải tích cổ điển luyện thi cao học Đại Học Cần Thơ

Người soạn: Nguyễn Anh Quốc Trang 20





















 












 

 







 

 



 

 
















  
  



 

 







































































    

  
Gii
m ti hn thuc min trong c



  

  








 

 


Gii h 










  

  




 

 






    





    















































  







  
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

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
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


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





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





    

  








m ti hn thuc min trong c nht OABC




    



    
Gii h 





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
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    













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




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










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
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












6
4
2
-2
-10
-5
5
10
B
A
O
4
2
-2
-4
-10
-5
5
10
C
A
B

O
Bài tập giải tích cổ điển luyện thi cao học Đại Học Cần Thơ

Người soạn: Nguyễn Anh Quốc Trang 21












     

 














 









































 

 


















 














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
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






 ln nh nht c


 

 



  






     




 


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









 






 
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

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 
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
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

  
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
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


 



Gii


 

 


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  

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 

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
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Gii h 
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


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


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





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


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



 




  



 






 

  



  



 


















   


   


 



  



 








 



 



  



 

Bài tập giải tích cổ điển luyện thi cao học Đại Học Cần Thơ

Người soạn: Nguyễn Anh Quốc Trang 22


























































     
m ti hn thuc min trong c



   


  
Gii h 











   
  

























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










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
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  




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
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




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Gii h 
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 
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    
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 



2
-2
-4
-10
-5
5
10

C
B
A
O
Bài tập giải tích cổ điển luyện thi cao học Đại Học Cần Thơ

Người soạn: Nguyễn Anh Quốc Trang 23


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    
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


Gii
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    
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Ta tm ti hn thuc min trong ca D
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
2
1
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4
6
m
O
A
4

2
-2
-4
-10
-5
5
10
B
A
O
Bài tập giải tích cổ điển luyện thi cao học Đại Học Cần Thơ

Người soạn: Nguyễn Anh Quốc Trang 24

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