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Bài tập Đồng điệu cực trị hàm số môn Toán 12

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Bài tập Đồng điệu cực trị hàm số môn Toán 12. Tài liệu được sưu tầm giúp bạn tham khảo, ôn tập và đạt kết quả cao. Mời bạn đọc đón xem.

Chủ đề: Chương 1: Ứng dụng đạo hàm để khảo sát và vẽ đồ thị của hàm số 389 tài liệu

Môn: Toán 12 4.5 K tài liệu

Tác giả:

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/19
6
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f x
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1 2 1 2
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x y
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18
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3 2
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y x
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y x
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x
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tan
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22
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5; +¥
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siny x x= - +
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)(xfy
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2018.21)(
+
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23
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y f x=
¡
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=y f x
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x
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x
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(
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y f x=
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y f x=
[
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f x
4, 1x x
= - = -
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y f x=
3
2
1
0
3
2
1
1
3
2
0
x
2
2
4
y
1-1-2
2
3 2
y ax bx cx d= + + +
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24
( )
y f x=
( )
f x
4
3
2
5
(
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=y f x
1= -y
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0=x
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y f x=
[ ]
1;3-
0x = 2x =
0x = 3x =
0x = 1x = -
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3
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1; 7-
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x
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1
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x
y
x
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+
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y x
=
3
y x x
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2
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M
n
2
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2
x x
y
x
+ +
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x =
10 3
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3
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3
4
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=
3
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x =
3
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5
1,
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x x
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1
2
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y
25
sin 2y x x
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p
3
.
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p
+
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p
+
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p
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=
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2
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=
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- +¥
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=
1x
=
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=
2x
= -
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=
( 2;1)
-
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¢
= - - -
2
1
0 3
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f x
¡
(
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f x
¢
(
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f x
1
2
2 3
2 1
x x
y
x
+ +
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+
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= +
1y x
= +
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= +
1y x
= -
2
3 4 5
1
x x
y
x
- +
=
-
1y x
= +
6 4y x
= - +
6 4y x
= +
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= -
3 2
1
2 3
3
y x x x= - +
2 3 6 0x y
- + + =
2 3 9 0x y
+ + =
2 3 6 0x y
+ - =
2 3 9 0x y
- + =
26
(
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y f x=
¡
(
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f x
¢
(
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(
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1 1y g x f x= = - +
(
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y g x=
(
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; 2-¥ -
(
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y g x=
(
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1;+¥
(
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y g x=
(
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2;- +¥
(
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y g x=
(
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2;1-
(
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y f x=
(
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'
y f x=
(
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(
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3g x f x= -
(
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4;7
(
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2;3
(
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; 1-¥ -
(
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1; 2-
27
(
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y f x=
¡
(
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(
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(
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'y f x=
( )
(
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2
y f x=
(
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2; 1- -
3
1;
2
æ ö
-
ç ÷
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(
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1;1-
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1;2
(
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f x
¡
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y f x
¢
=
(
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(
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2
2 3 1 9 6 4h x f x x x= + - - +
(
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h x
¡
(
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h x
1
1;
3
æ ö
-
ç ÷
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(
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h x
1
1;
3
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ç ÷
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(
)
h x
¡
28
( )
3 2
y f x x ax bx c= = + + +
( )
1, 1 3x f= = -
2.x = -
( )
2 16.f - =
( )
2 24.f - =
( )
2 2.f - =
( )
2 4.f - =
4 2
( )y f x ax bx c= = + +
( )
0; 2A
( )
2; 14B -
( )
1f
( )
1 6f = -
( )
1 0f =
(
)
1 7f = -
(
)
1 5f = -
( )
y f x
=
¡
( )
y f x
¢
=
( ) ( )
3g x f x x= +
(
)
f x
( ) ( ) ( ) ( )
2 3 4
' 1 2 3f x x x x x= - - -
(
)
3
f x
1
2
4
3
29
( )
y f x
=
¡
( )
y f x
¢
=
( )
2
3y f x= -
4 2
5 3
( )
y f x=
¡
( )
y f x
¢
=
( )
2017 2018 2019y f x x= - - +
3
1 4 2
( )f x
( )
y f x
=
¡
( )
y f x
¢
=
( ) ( )
3g x f x x= +
(
)
y f x
¢
=
( ) ( )
3
2
2
3
x
g x f x x x= - + - +
2x
=
0x
=
1x
=
1x
= -
(
)
f x
( ) ( ) ( ) ( )
2 3 4
' 1 2 3f x x x x x= - - -
(
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3
f x
1
2
4
3
x
y
-2
2
O
1
30
( )
y f x
=
¡
( )
y f x
¢
=
( )
2
3y f x= -
4 2
5 3
(
)
y f x=
¡
(
)
y f x
¢
=
(
)
2017 2018 2019y f x x= - - +
3
1
4 2
( )f x
(
)
y f x
¢
=
( ) ( )
3
2
2
3
x
g x f x x x= - + - +
2x
=
0x
=
1x
=
1x
= -
x
y
-2
2
O
1

Tài liệu khác của Toán 12

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y = f '( x). f ( x ) y = f (x) ¡ 1 x , x2 Î ¡ Þ f ( 1 x ) < f ( x2 ) 1 x < 2 x Î ¡ Þ f ( 1x) < f ( 2 x ) 1 x , x2 Î ¡ Þ f ( 1 x ) > f (x2 ) 1
x > x2 Î ¡ Þ f ( 1x) < f (x2 ) (0; )1 (2;+¥) (1;2) (2;+¥) (0; )1 y = f ( x) (a;b) y = f ( x) (a;b) f ¢(x) > 0,"x Î (a;b). f ¢( x) < 0,"x Î(a;b) y = f ( x) (a;b) y = f ( x) [a;b] f ¢( x) > 0,"x Î(a;b) y = f ( x) [a;b] 3 2 y = x +3x -4 3 0 2 1 ( 2 - ;0) (- ; ¥ 2 - ) (0;+¥) ¡ y = f (x) f '(x) > 0, "x Î ¡ x 1 f ( ) < f (1) -x+2 x y = ( x-1 -¥; 0) È (0;1) (-¥;1) (-¥;0) È(1;+¥) (0;1) (-¥; ) 1 (1;+¥) (-¥ ) ;1 (1;+¥) ¡ x¹1 6 4 2 y = x - 2x -1 y = sin x -cos x + 3x (- ; ¥ - ) 1 (-¥;0) (0;1) (1;2) (0;+¥) (- ; ¥ - ) 1 (-¥;+¥) (0;1) ( 1 - ;0) 2x - 3 y = 2 x -1 (-¥;- ) 1 æ 3 1; ö æ 3 ö ç ç ;+¥ 2 ÷ ÷ è ø è 2 ø æ 3 1; ö ç ÷ (-¥;- ) 1 è 2 ø + 3 x 1 y = x - x +1 y = x-1 3 y = x + 2x-3 4 2 y = x + 2x +3 y = f (x) f ¢(x) f (x) ( 2 - ;0) f (x) (0;+¥) f (x) (- ; ¥ 3) 2 y = 2x - x f (x) ( 3 - ;- 2) (- ; ¥ 2) (0;1) (1;2) (1;+¥) 7 y = f (x) f ( x) ¡ f (x) 2 ' = x +1 "x Î ¡ y = f '( x) (1;+¥) ( 1 - ; ) 1 f ( x) (-¥;0) (1;2) (- ; ¥ +¥) f ( x) (0;2) f ( x) (-2 ) ;1 f ( x) ( 1 - ; ) 1 y = (x + )( x - )2 2 1 y = x + (x - )2 2 1 (- ; ¥ - ) 1 . ( 1 - ;2). y = f (x) f ¢( x) = x( x - )2 ( x + )3 1 1 ( x- 2) y = f (x) (- ; ¥ 2 - ). (- ; ¥ - ) 1 (0; )1 (1;+¥) ( 1 - ;0) ( 2 - ;0). 2 y = 2 x +1 (0;+¥) ( 1 - ; ) 1 (- ; ¥ +¥) (- ; ¥ 0) 8 y = f ( x) ¡ y = f ( x) ¡ f ¢(x) f (2) = f (-2) = 0 y = f '(x) y = g( x) = f (1- x) +1 y=g( )x (- ; ¥ - ) 2 y=g( )x (1;+ ) ¥ y=g( )x ( 2 - ;+ ) ¥ = ( ( ))2 y f x y=g( )x ( 2 - ) ;1 ( 2 - ;- ) 1 æ 3 1; ö - ç 2 ÷ è ø ( 1 - ; ) 1 (1;2) f x y = f ( x) ( ) ' y = f (x) g( ) x = f ( 3-x) y = f ( - ) 2 2 1 x + x 1 + - x (4;7) (2; )3 (- ;1 ¥ ) (- ; ¥ 2 - ) (-2;0) (- ; ¥ - ) 1 ( 1 - ;2) ( 3 - ; 2 - ) 9 f ( x) ¡ y = f ¢(x) h(x) = f ( x + ) 2 2 3 1 -9x -6x +4 y = f (x) y = f ( 2 2 - x ) ( 1 - ;0) (1;+¥) h(x) ¡ ( 2 - ; ) 1 (0 ) ;1 . æ 1 ö h(x) 1 - ç ; 3÷ è ø æ 1 ö h(x) 1 - ç ; 3÷ è ø h(x) ¡ 10 3 2 y = mx +3mx -(m - ) 1 x -4 m æ 1 é 1 0; ö é 1 ù æ 1 ù ö ç 0; ç 0; 0; 4 ÷ ê ÷ è ø ê 4ú ë û 4 ú è û ë 4 ø 3 2 y = x + 2x -3x +1 26x + 9 y - 15 = 0 -25x + 9 y -15 = 0 26x - 9 y + 15 = 0 25x - 9 y +15 = 0 17 3 2 y = x - 3x +3(1- m) x +1+ 3m D : 2mx + y - 2m - 2 = 0 D : 2mx + y - 2m - 2 = 0 D : y = 202 - 200x D : y = 202 - 200x 18 y = f (x) f ( x) ¡ 1 x , 2 x Ρ Þ f ( 1x) < f ( 2 x ) 1 x < 2
x Î ¡ Þ f ( 1x) < f (x2 ) 1 x , 2 x Ρ Þ f ( 1x) > f ( 2 x ) 1 x > 2 x Ρ Þ f ( 1x) < f ( 2 x ) (0;3) (0;4) (-2;3) (-2;0) y = f ( ) x f '( ) x > 0,"xΡ x 1 f ( ) < f (1) x + (-¥;0) È(0;1) (- ;1 ¥ ) ( ) ax b f x = cx+d (- ; ¥ 0) È(1;+¥) (0;1) y 1 O 1 x f (x) ¡ f ¢(x) > 0 "xÎ(0;+¥) f ( ) 1 > f (2) f (3) > f ( ) 1 f ( ) 1 > f (- ) 1 (-¥ ) ;1 (1;+¥) æ 4 ö æ 5 f ÷ f ö > ç (- ; ¥ - ) 1 3 ç 4 ÷ è ø è ø (1;+¥) 2 1 0 3 f ( x) y = f (x) f ¢( x) > 0,"xÎ ¡ f (2) = 1 x – -1 0 + f (0) < f (3) f (4) + f (3) = 2 y' – 0 + 0 – 0 + f ( ) 1 < 1 1 < f (4) + 2 + y -2 -2 y = f ( x) ( 2 - ;+¥) (- ; ¥ 2 - ) ( 1 - ;0) ( 2 - ;2) 19 y = f ( x) ¡ \{ } 0 y = f ( x) 2 y' = x ( x- 2) (- ; ¥ 0) (2;+¥) (2;+¥) (0;2) ¡ (0 ) ;1 ( -1; ) 1 (-1;0) ( 1 - ;+¥) y = f (x) R y = f ¢( x) y y = f ( x) y = f (x) ( ;ab) (- ; ¥ - ) 2 y = f (x) (1;5) O a x1 x2 x3 b x y = f (x) (-1;1) y = f (x) (-1; )1 y = f (x) > 0,"Î(a;b) f ¢(x > 0 1) f ¢( x > 0 2 ) (x ;x 2 3 ) 20 y = f '(x). 3 2 y = -x +3x +1 y = f ( x) (0;+¥) (0;2) (-¥;2) (-¥;0) (2;+¥) (0;1) (2;+¥) (1;2) (2;+¥) (0; ) 1 4 3 y = x - 4x + 3 (- 2;0),( 2;+¥) (- ;¥- 2),(0; 2) (3;+¥) (0;3) 2x +1 y = x-1 ¡ \ { } 1 1 y = x- . 4 2 y = 2x + 4x + 2019. ( x -¥; ) 1 2- x ( 3 2 1;+¥) y = . y = x -4x 1 - 1 . x x +3 (-¥; ) 1 È (1;+¥) (-¥;1) (1;+¥) ¡ 4 2 y = x - 2x +3 3 2 y = x + 3x + 2x+1 y = tan x 3 y = x +3x - 4 - y = f (x) 2 = -x+1 ¡¡ 21 2 y = x - 4x - 5 y = (x + )( x - )2 2 1 (5;+¥) (2;+¥) (- ; ¥ - ) 1 y = x + ( x - )2 2 1 ( ; -¥ 2) ( ; -¥ - ) 1 . (-1;2). (-¥;-2). (-2;0). 2 y = -x + sin x ¡ (1;2) Æ (-¥;2) y = f (x) ¡ f ¢(x)
f ¢(x) = (1 - x)(x + 2).g(x)+ 2018 g (x) < 0, x " Î ¡ y = f 1 ( - x) + 2018x + 2019 ( ;1+¥) ( ) 3 ; 0 (- ) ( + ; 3 ¥) 3 ; ¥ y = f ( x) -x + 2 + y = x 2 y = x -1 x -1 x + 2 - y = x 3 y = x +1 x -1 5 2 0 1 22 f (x) y = f (x) [ 4 - ;0] f ( x) x = 2 - x = 3 x = 1 x = 2 ¡ x = 4, - x = 1 - x = -3 x = -1 x = 0 y = f (x) y 2 x x = 0 -2 -1 1 2 x = 2 2 4 y = f (x) ¡ 3 2 1 0 3 2 y = ax + bx + cx + d (a,b, c, d Ρ) y = f (x) 1 y = f (x) 0 1 y = f (x) x = 0 3 2 1 x = 1 y = f (x) y = f (x) 1 3 2 0 x = 1 x = 0 x = 5 x = 2 23 y = f (x) x 1 y - = 4 y = x x +3 3 y = -x + x 2 y = x + 2x+2 f (x) M n 4 3 2 5 2 x + 3x + 3 y = f ( x) y = x + 2 2 M - 2n y = 1 - -1 2 x = 0 y = x - 2 x + 4. y = f (x) y 2 - 3. [ 1 - ;3] 2 3 x = - . 3 1 O 2 3 x 2 3 x = . 3 x = 0 x = 2 10 3 - x . = 0 x = 3 3 x = 0 x = -1 x = 1 - x = 2 3 y = x -3x +5 ( 1 - ;7) (1;3) (7;- ) 1 (3; )1 2 y = -2x +3x + 5 3 - x = 3 x = 4 4 3 3 x = 5 x 1, x - = = x 2 2 y = - 2x + 3x + 2 2 3 3 æ 2 0; ö æ 2 ö ç (1;2) ( 1 - ;2) ç3; 3 ÷ ÷ è ø è 3 ø 24 f (x) ¡ f ¢( x) f (x) y = x + sin 2x (0;p ) p 3 p + . 2 3 + . 6 2 3 2 2p 3 p - . 3 + . 3 2 3 2 1 2 x + 2x +3 y = 2x+1 y = 2x + 2 y = x +1 y = 2x +1 y = 1- x y = f ( ) x ¡ 2 f '(x) = (x + 2)(x-1) y = f ( ) x (-2;+ ) ¥ 2 3x - 4x +5 y = y = f ( ) x x = 1 x -1 y = f (x) x = -2 y = f ( ) x (-2;1) y = x +1 y = -6x + 4 y = 6x + 4 y = 6x - 4 f ( x) 1 2 3 4
f (¢x) = x(x -1) (x - 2) (x -3) 3 2 y = x - 2x + 3x 3 -2x + 3y + 6 = 0 2 1 0 3 2x + 3y + 9 = 0 2x + 3y - 6 = 0 2x - 3y + 9 = 0 25 y = f ( x) ¡ y = f ( x) f ¢(x) ' y = f ( x) g( )x = f ( 3-x) y = g (x) = f (1- x) +1 y = g(x) (- ; ¥ - ) 2 y = g(x) (1;+¥) y = g(x) ( 2 - ;+ ) ¥ y = g(x) (-2;1) (4;7) (2; )3 (- ; ¥ - ) 1 (-1;2) 26 y = f (x) ¡ f (x) ¡ f (2) = f (-2) = 0 y = f '(x) y = f ¢( x) h(x) = f ( x + ) 2 2 3 1 - 9x - 6x + 4 =( ( ))2 y f x ( 2 - ;- ) 1 æ 3 1; ö - ç 2 ÷ è ø ( 1 - ) ;1 (1;2) h(x) ¡ æ 1 ö h(x) 1 - ç ; 3÷ è ø æ 1 ö h(x) 1 - ç ; 3÷ è ø h(x) ¡ 27 = ( ) 3 2 y f x = x + ax + bx+ c f ( x) x =1, f ( ) 1 = 3 -
f ( x) = x( x - )2 ( x - )3 ( x - )4 ' 1 2 3 3 f (x) x = 2. - f ( 2 - ) =16. f ( 2 - ) = 24. 1 2 4 3 f ( 2 - ) = 2. f ( 2 - ) = 4. y = f (x) ¡ 4 2 y = f ( ) x = ax +bx + c y = f ¢(x) A(0;2) B (2; 1 - 4) f ( ) 1 g (x) = f ( x) + 3x f ( ) 1 = -6 f ( ) 1 = 0 f ( ) 1 = -7 f ( ) 1 = -5 28 y f (x) y = f (x) ¡ y = f ¢(x) y = f ¢(x) 2 3 -2 1 x g ( x) = f ( x) x 2 y - + x - x + 2 = f ( 2 x - 3) O 3 x = 2 x = 0 4 2 5 3 x =1 x = 1 - f ( x) y = f (x)
f ( x) = x( x - )2 (x - )3 ( x - )4 ' 1 2 3 ¡ 3 f (x) y = f ¢( x) 1 2 4 3
y = f (x - 2017) - 2018x + 2019 3 1 4 2 y = f (x) ¡ y = f ¢(x) g (x) = f (x) + 3x 29 y = f (x) y ¡ y = f ¢(x) f (x) 2 y = f ¢(x) y = f ( 2 x - ) 3 -2 1 x O 4 2 5 3 3 g ( x) = f ( x) x 2 - + x - x + 2 3 x = 2 x = 0 x =1 x = 1 - y = f ( x) ¡ y = f ¢(x)
y = f (x - 2017) - 2018x + 2019 3 1 4 2 30

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