Методичка Исследование функций

f x =

x

2

x 1

1

x 1

f x = x 2

2

2x 7

2

x

2x 3

3

f x =

4 x3

x2

4

f x =

4x

x 1

2

f x =

2x

3

1

5

x

2

6

f x =

2x 3 e

2 x 1

7

f x =

3 x

e

x 2

8

x 6

1

f x = ln

x

9

e

f x =

2 x 1

2 x 1

f x =

10

x 4

e

( x 3)

11

f x =

3

x2 x 2

2

12

f x =

3

x2 x 2

2

13

f x =

3

(x

2

2x 3)

2

14

f x = 3

x2 x 3

15

f x =

3 (x 1) x 2

2

16

f x = 3 x x 3 2

z x, y

= x

3

2xy

y

2

4x

z x, y

= x2 2xy

5

y2 2x

2

z x, y

= x2 2xy 10

z x, y

= x

2

2xy

y

2

2x 2 y

z x, y

= 6xy 9x

2

9 y

2

4x 4y

z x, y

= x

2

xy 2

z x, y

= 2x

2

2xy

1

y

2

4x

2

z x, y

= 5x

2

3xy y

2

4

z x, y

= x

2

2xy

y

2

4x

z x, y

= x

2

2xy

y

2

4x 1

z x, y

= 3x

3

y

3

4xy x 2

x

2

y

2

xy 9y

6x 35

6x

2

7xy 2 y

2

6x 3y

4x

2

5xy 3y

2

9x 8y

x3

xy

2 3xy

x2

2x y2 3y

3

2

f x =

2

x 2

x

4

y

4

2x

2

4xy 2y

2

x

3

2

3

3

2

f x =

x x 1

x

y

12 x y

2

f x =

x

2

2

(x 3)

2

x

3

y

2

6xy

39x 18y 20

3

3

f x =

3

x x 6

2

14x

3

27xy

2

69x 54y

f x

3x

2

10

x

2

2 y y

2

4x

2

1

f x

3x

2

10

x

2

y

2

2x

3 2x

f x

x

2

2x 2

2xy 4x 2 y

x 3

f x

8 x

2

x

3

6xy 8y

3

1

x

2

4

f x

4x

3

3x

x

e

x y

2

2

4x

2

1

f x

x

2

3

2xy 3x

2

2 y

2

10

3x

2

2

f x

2x

2

1

x

2

y

2

4x 4y

x

2

2

f x

x2 11

x2 xy y2 x y 1

4x 3

f x

x

2

2x 1

x

2

2xy 4x 8y

2x 1

f x

2 x2

2xy 4x 2y2

9x

2

4