Ngọc huyền LB phong tỏa VD VDC buổi 2 tìm điều kiện của tham số m để hàm số có cực trị thỏa mãn điều kiện cho trước (handout)

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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 2 – TÌM ĐIỀU KIỆN CỦA THAM SỐ m
ĐỂ HÀM SỐ CÓ CỰC TRỊ TMĐK CHO TRƯỚC

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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



Dạng 1. Tìm m để hàm số đạt cực trị tại x=x0
BON 01 Có bao nhiêu giá trị nguyên của tham số m để hàm số





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y  x3  mx 2  m2  m  1 x  1 đạt cực đại tại x  1 ?
3
A. 0.
B. 2.
C. 1.

D. 3.

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BON 02 Tìm tất cả các giá trị của tham số m để hàm số y  x3  3x2  mx  1 đạt
A. m  0 .

B. m  4 .

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cực tiểu tại x  2.

C. 0  m  4 .

D. 0  m  4 .

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LIVESTREAM PHÁC ĐỒ TOÁN 12

BON 03 Cho hàm số y  f  x  xác định trên tập số thực

 QUICK NOTE



f   x    x  sin x  x  m  3  x  9  m2

 x 

và có đạo hàm

3

( m là tham số). Có bao nhiêu giá

trị nguyên của m để hàm số y  f  x  đạt cực tiểu tại x  0 ?
A. 6.

B. 7.

C. 5.

D. 4.

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 QUICK NOTE

LIVESTREAM PHÁC ĐỒ TOÁN 12

BON 04 Tất cả các giá trị thực của tham số m để hàm số y 

x 5 mx 4

 2 đạt
5
4

cực đại tại x  0 là
A. m .

B. m  0 .

C. Không tồn tại m .

D. m  0 .

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LIVESTREAM PHÁC ĐỒ TỐN 12

BON 05 Có bao nhiêu giá trị nguyên của m thuộc khoảng  2019; 2019  để

 QUICK NOTE

m1 5 m 2 4
x 
x  m  5 đạt cực đại tại x  0 ?
5
4

A. 101.
B. 2016.
C. 100.

hàm số y 

D. 10.

 LỜI GIẢI
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 QUICK NOTE

LIVESTREAM PHÁC ĐỒ TỐN 12

BON 06 Có bao nhiêu giá trị nguyên của tham số m để hàm số





y  x12   m  5 x7  m2  25 x6  1 đạt cực đại tại x  0 ?

A. 8.

B. 9.

C. Vô số.

D. 10.

 LỜI GIẢI
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 QUICK NOTE

LIVESTREAM PHÁC ĐỒ TỐN 12

BON 07 Có bao nhiêu giá trị nguyên của tham số m để hàm số





y  x8   m  1 x5  m2  1 x4  1 đạt cực tiểu tại x  0?

A. 3.

B. 2.

C. Vô số.

D. 1.

 LỜI GIẢI

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LIVESTREAM PHÁC ĐỒ TỐN 12

Dạng 2. Tìm m để hàm số có n cực trị

 QUICK NOTE

BON 08 Cho hàm số y  x3  3  m  1 x2  3 7m  3 x . Gọi S là tập các giá trị
nguyên của tham số m để hàm số khơng có cực trị. Số phần tử của S là
A. 2 .

B. 4 .

C. 0 .

D. Vô số.

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BON 09 Cho hàm số f  x  có đạo hàm f   x   x2  x  1  x2  2mx  5 . Có tất cả
A. 0 .

C. 6 .

D. 7 .

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 LỜI GIẢI

B. 5 .

ay

bao nhiêu giá trị nguyên của m để hàm số có đúng một điểm cực trị?

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 QUICK NOTE

BON 10

LIVESTREAM PHÁC ĐỒ TOÁN 12

Hàm số y  mx4   m  1 x2  1  2m có một điểm cực trị khi
B. m  0  m  1 .

A. 0  m  1 .

D. m  0  m  1 .

C. m  0 .

 LỜI GIẢI
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Có tất cả bao nhiêu giá trị nguyên của m trên miền 10;10 để hàm

ay

BON 11

số y  x4  2  2m  1 x2  7 có ba điểm cực trị?
C. Vơ số.

D. 11 .

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 LỜI GIẢI

B. 10 .

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A. 20 .

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 QUICK NOTE

BON 12

LIVESTREAM PHÁC ĐỒ TOÁN 12

Cho hàm số f  x  có đạo hàm

f   x   x2  x  2   x  4   x2  2  m  3  x  6m  18  .
4

3

Có tất cả bao nhiêu giá trị nguyên của m để hàm số f  x  có đúng một điểm cực
trị?

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A. 7 .

B. 5 .

C. 8 .

D. 6 .

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LIVESTREAM PHÁC ĐỒ TỐN 12

Dạng 3. Tìm m để hàm số bậc 3 có cực trị thỏa mãn điều kiện cho trước

 QUICK NOTE

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1
Cho hàm số y  x3  mx 2  4 x  10 , với m là tham số; gọi x 1 , x 2 là
3
2
các điểm cực trị của hàm số đã cho. Giá trị lớn nhất của biểu thức

BON 13







P  x12  1 x22  1 bằng

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A. 4 .

B. 1 .

C. 0 .

D. 9 .

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BON 14 Biết m0 là giá trị của tham số m để hàm số y  x3  3x2  mx  1 có hai
C. m0   15; 7  .

D. m0   7; 1 .

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 LỜI GIẢI

B. m0  7;10  .

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A. m0   1;7  .

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điểm cực trị x1 , x 2 sao cho x12  x22  x1x2  13 . Mệnh đề nào dưới đây đúng?

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 QUICK NOTE

BON 15

LIVESTREAM PHÁC ĐỒ TỐN 12

a
a
(trong đó

là phân số tối giản và a, b * ) là giá trị của tham
b
b

Biết





2
2
số m để hàm số y  x3  mx 2  2 3m2  1 x  có 2 điểm cực trị x 1 , x 2 sao cho
3
3

x1x2  2  x1  x2   1 . Tính giá trị biểu thức S  a2  b2 .

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B. S  25 .

A. S  13 .

D. S  34 .

C. S  10 .

 LỜI GIẢI
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Cho hàm số y  2x3  3  m  1 x2  6  m  2  x  1 với m là tham số thực.

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BON 16

khoảng  2; 3 .

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 LỜI GIẢI

D. m  1; 4  .

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C. m  3; 4  .

B. m 1; 3 .

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A. m  1; 3   3; 4  .

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Tìm tất cả các giá trị của m để hàm số có điểm cực đại và điểm cực tiểu nằm trong

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 QUICK NOTE

LIVESTREAM PHÁC ĐỒ TOÁN 12

m 3
x   m  1 x2  3  m  2  x  2 . Hàm số đạt cực trị tại
3
x1 , x 2 thỏa mãn x1  2 x2  1 khi m  a và m  b . Hãy tính tổng a  b .

BON 17

Cho hàm số y 

8
A.  .
3

B.

8
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3

5
C.  .
2

D.

5
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Tổng tất cả các giá trị thực của tham số m để hàm số:

H

BON 18

y  x1  .y  x2   0 là

x1 ; x 2

đồng thời

D. 3 11  13.

C. 8.

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 LỜI GIẢI

B. 39.

M

A. 21.

có hai điểm cực trị

ay

y  3x3  2  m  1 x2  3mx  m  5

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BON 19

LIVESTREAM PHÁC ĐỒ TỐN 12

Tìm tất cả các giá trị của tham số thực m sao cho đồ thị hàm số

y  x3  5x2   m  4  x  m có hai điểm cực trị nằm về hai phía đối với trục hoành.
B.  ; 3   3; 4 . C.  ; 3   3; 4  .

A.  .

D.  ; 4  .

 LỜI GIẢI
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BON 20 Có bao nhiêu giá trị nguyên của tham số m để đồ thị hàm số

A. 4.

C. 1.

D. 3.

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 LỜI GIẢI

B. 2.

ay

hoành?

H

y  mx3   2m  1 x2  2mx  m  1 có hai điểm cực trị nằm về hai phía của trục

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 QUICK NOTE

BON 21

LIVESTREAM PHÁC ĐỒ TOÁN 12

Gọi S là tập hợp tất cả các giá trị thực của tham số m để đồ thị của





1
hàm số y  x3  mx2  m2  1 x có hai điểm cực trị A và B sao cho A, B nằm
3
khác phía và cách đều đường thẳng d : y  5x  9. Tính tổng tất cả các phần tử của S.

A. 3 .

C. 6 .

B. 6 .

D. 0 .

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LIVESTREAM PHÁC ĐỒ TỐN 12

Một số bài tốn có điều kiện hình học

 QUICK NOTE

BON 22 Tìm tất cả giá trị thực của tham số m để đồ thị hàm số y  x3  3mx2  2
có hai điểm cực trị A và B sao cho các điểm A , B và M 1;  2  thẳng hàng.

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A. m  2 .

B. m   2 .

C. m  2 .

D. m   2; m  2 .

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BON 23 Cho hàm số y  x3  3mx2  3m  1 với m là một tham số thực. Giá trị
của m thuộc tập hợp nào sau đây để đồ thị hàm số đã cho có hai điểm cực trị đối

M

xứng nhau qua đường thẳng d : x  8 y  74  0.
C. m   3; 5 .

D. m  1; 3 .

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 LỜI GIẢI

B. m   3; 1 .

ie

A. m   1;1 .

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 QUICK NOTE

LIVESTREAM PHÁC ĐỒ TỐN 12

BON 24 Tìm tất cả các giá trị thực của tham số thực m để đường thẳng đi qua
hai điểm cực đại, cực tiểu của đồ thị hàm số y  x3  3mx  2 cắt đường trịn  C 

có tâm I 1;1 , bán kính bằng 1 tại hai điểm phân biệt A, B sao cho diện tích tam
giác IAB đạt giá trị lớn nhất.

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A. m 

2 3
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3

B. m 

2 3
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2

C. m 

1 3
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2

D. m 

2 5
.
2

 LỜI GIẢI
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LIVESTREAM PHÁC ĐỒ TOÁN 12

BON 25 Gọi A, B là hai điểm cực trị của đồ thị hàm số f  x   x3  3x  4 và

 QUICK NOTE

M  x0 ;0  là điểm trên trục hồnh sao cho tam giác MAB có chu vi nhỏ nhất, đặt
T  4 x0  2015 . Trong các khẳng định dưới đây, khẳng định nào đúng?

B. T  2019 .

A. T  2017 .

D. T  2018 .

C. T  2016 .

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