Ngọc huyền LB phong tỏa VD VDC buổi 1 tìm điều kiện của tham số m để hàm số đơn điệu trên k (handout) (1)

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LIVESTREAM PHÁC ĐỒ TOÁN 12
Ngày học ___/___/___

HỆ THỐNG ĐÀO TẠO
TOÁN NGỌC HUYỀN LB

PHÁC ĐỒ TOÁN 12 SEASON 2023

Sưu tầm & biên soạn

PHONG TỎA VD-VDC
BUỔI 1 – TÌM ĐIỀU KIỆN CỦA THAM SỐ m
ĐỂ HÀM SỐ ĐƠN ĐIỆU TRÊN K

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BON
(viết tắt: the Best Or Nothing).
Cơ mong các trị ln khắc cốt
ghi tâm khí chất BONer:

"Nếu tơi quyết làm gì, tơi sẽ làm
nó một cách thật ngoạn mục,
hoặc tơi sẽ khơng làm gì cả”.

 QUICK NOTE



BON 01 Tìm tất cả các giá trị của m để hàm số y   m  1 x3  3  m  1 x2  3x  2
đồng biến biến trên

.

B. 1  m  2 .

A. 1  m  2 .

D. 1  m  2 .

C. 1  m  2 .

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 LỜI GIẢI
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A. 5.

là
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đồng biến trên

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BON 02 Số giá trị nguyên của m để hàm số y   4  m2  x3   m  2  x2  x  m  1
C. 2.

D. 4.

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 LỜI GIẢI

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 QUICK NOTE

LIVESTREAM PHÁC ĐỒ TOÁN 12

BON 03 Tổng bình phương của tất cả các giá trị nguyên của tham số m để hàm





số y  3m2  12 x3  3  m  2  x2  x  2 nghịch biến trên
A. 9.

B. 6.

là

C. 5.

D. 14.

 LỜI GIẢI
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BON 04 Có bao nhiêu giá trị nguyên của tham số m để hàm số y 

C. 1.

D. 3.

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B. Vô số.

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A. 2.

M

biến trên khoảng  ; 10  ?

x2
đồng
x  5m

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 QUICK NOTE

LIVESTREAM PHÁC ĐỒ TỐN 12

BON 05 Có bao nhiêu giá trị nguyên của tham số m để hàm số y 
nghịch biến trên khoảng  0; 4  ?
A. 5.

B. 11.

C. 6.

mx  9
4x  m

D. 7.

 LỜI GIẢI
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BON 06 Gọi S là tập hợp các giá trị nguyên dương của m để hàm số
của S bằng

C. 3.

D. 0.

ay

 LỜI GIẢI

B. 2.

H

A. 1.

oc

y  x3  3  2m  1 x2  12m  5 x  2 đồng biến trên khoảng  2;   . Số phần tử

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LIVESTREAM PHÁC ĐỒ TOÁN 12

BON 07 Cho hàm số f  x   x3   m  1 x2   2m2  3m  2  x  2. Có bao nhiêu

 QUICK NOTE

giá trị nguyên của tham số m sao cho hàm số đã cho đồng biến trên khoảng

 2;   ?
A. 2.

B. 3.

C. 4.

D. 5.

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BON 08 Gọi S là tập hợp tất cả các giá trị của tham số m để hàm số





ay

1
1
f  x   m2 x5  mx 3  10 x 2  m2  m  20 x đồng biến trên
5
3
tất cả các phần tử thuộc S bằng

C.

1
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2

D.

3

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2

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B. 2.

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2

M

A.

. Tổng giá trị của

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 QUICK NOTE

BON 09 Cho hàm số y 

 4  m

LIVESTREAM PHÁC ĐỒ TỐN 12

6x 3

6x m

. Có bao nhiêu giá trị nguyên của m

trong khoảng  10;10  sao cho hàm số đồng biến trên  8; 5 ?
A. 14.

B. 13.

C. 12.

D. 15.

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Cho hàm số y 

ln x  4
với m là tham số. Gọi S là tập hợp các giá
ln x  2m

H

BON 10

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trị nguyên dương của m để hàm số đồng biến trên khoảng 1;e  . Tìm số phần tử
A. 3.

C. 1.

D. 4.

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 LỜI GIẢI

B. 2.

M

của S.

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 QUICK NOTE

BON 11
y  3x 

LIVESTREAM PHÁC ĐỒ TỐN 12

Có tất cả bao nhiêu giá trị ngun của tham số m để hàm số
m2  3m
đồng biến trên từng khoảng xác định của nó?
x1

A. 4.

B. 2.

C. 1.

D. 3.

 LỜI GIẢI
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BON 12

Có bao nhiêu giá trị nguyên của m để hàm số

H

cos 2 x  2 m cos x  m2  100
đồng biến trên khoảng
cos x  m

A. 18.

B. 10.

C. 20.

 
 0;  ?
 2
D. 19.

ay

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 LỜI GIẢI

oc

y

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 QUICK NOTE

BON 13

LIVESTREAM PHÁC ĐỒ TOÁN 12

Tập hợp tất cả các giá trị của tham số

y  x3   m  1 x2  x  m nghịch biến trên khoảng 1; 2  là


7
A.  ;   .
4



7
B.  ;   .
4


 7

C.  ;   .
 4


m

để hàm số

 7

D.   ; 1  .
 4


 LỜI GIẢI

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BON 14 Tập hợp các giá trị thực của tham số m để hàm số y  x  1 

m
đồng
x2

biến trên mỗi khoảng xác định của nó là
C. 0;   \1 .

D.  ;0  .

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B.  ;0 .

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A. 0;1 .

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 QUICK NOTE

BON 15

LIVESTREAM PHÁC ĐỒ TOÁN 12

Số các giá trị nguyên của tham số m thuộc đoạn 2021; 2021 để hàm

 
số y  cos3 x  cos2 x   m  2  cos x  7 đồng biến trên khoảng  0;  là
 2
A. 2019.

B. 2020.

C. 2021.

D. 2023.

 LỜI GIẢI

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 QUICK NOTE

BON 16



LIVESTREAM PHÁC ĐỒ TỐN 12

Tìm tập hợp tất cả các giá trị của tham số thực m để hàm số



y  ln x2  1   m  1 x đồng biến trên

A.  ; 2  .

B.  1;1 .

.

D.  ; 2 .

C. 1;1 .

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 QUICK NOTE

BON 17



LIVESTREAM PHÁC ĐỒ TOÁN 12



Cho hàm số y  mx4  2 m2  1 x2  m  1. Tìm m để hàm số đã cho

nghịch biến trên khoảng  2;   .

 LỜI GIẢI
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 QUICK NOTE

BON 18

LIVESTREAM PHÁC ĐỒ TOÁN 12

Cho hàm số y  f  x  , có đạo hàm trên

là

f   x   m2 x4  m m  2  x3  2  m  1 x2   m  2  x  m.
Số các giá trị nguyên dương của m để hàm số đồng biến trên
A. 1.

B. 3.

C. 0.

là
D. 2.

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GROUP FACEBOOK

 QUICK NOTE

BON 19

LIVESTREAM PHÁC ĐỒ TỐN 12

Tìm tất cả các giá trị thực của tham số

y   2m  2019  x   2018  m  cos2 x nghịch biến trên
B. m 

A. m  1.

4037
.
3

m

để hàm số

.

D. m  1.

C. m  1.

 LỜI GIẢI
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GROUP FACEBOOK

 QUICK NOTE

BON 20 Cho hàm số y 

LIVESTREAM PHÁC ĐỒ TOÁN 12

4 m 3 m2  4 m  3 2
x 
x  2m2  12m  6 x  m. Tìm m
3
2





để hàm số đồng biến trên khoảng  1;  .

 LỜI GIẢI
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GROUP FACEBOOK

 QUICK NOTE

BON 21

Cho hàm số y 



LIVESTREAM PHÁC ĐỒ TOÁN 12



1 3
3
m  1 x 4  x 3   m  2  x2  4 x  2022 (với m là
4
2

tham số). Số các giá trị nguyên của m thuộc đoạn 2021; 2021 để hàm số đã cho


1
đồng biến trên đoạn  1;   là
3


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A. 2022.

B. 2023.

C. 2024.

D. 2021.

 LỜI GIẢI
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