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&

()

2:

555 1

2.1 - 2.3

1. f

C f 0 0

(x ,y )

0 0 0 0

(x ,y ) (x ,f(x )) -

0

f (x ) f 0

x .

, : 0 0 0y f(x ) f (x )(x x )

:

f , :

) 0 0

A(x , f(x )) -

: .

) : , 0 0

M(x , f(x )),

0

x , 0

x -

.

1) (x0,f(x0)) Cf. [5 220, 7,B1,11 239]

) 0

f (x ) 0

f(x ) .

) 0 0 0

y f(x ) f (x )(x x ) .

2) ( ) , Cf. [10 239]

) 0 0M(x , f(x )) o -

():0 0 0

y y f (x )(x x ) .

(, , 0

x )

)

.

) 0

x

.

3) [3 228, 8,9,B2,6 239])

0 0M(x , f(x )) o .

) 0

f (x ) , 0

x .

) , , .

17

x0

M

Cff(x0)

A

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4) [A11, 2 239]

: y x f

C

0 0

M(x , f(x )) f

C -

:

) (),

0 0( )f x x .

) ()

f

C , 0

f (x ) .

5) [3 239]

0 0

M(x , f(x )) . -

f g

0

x :

)0 0

f(x ) g(x ) ,

fC gC , y f(x)

y g(x) ,

)0 0

f (x ) g (x ) , f

C g

C

.

0

x -

.

6) ()

f g.

() f

C g

C ,

,f( ()) ,g( ())

:

) f () g ()

) f

C ,f( ()),

,g( ()) . , -

.

7) () [4,10 239]

() f

C

,f( ()) g

C . ,g( ()) g

C

:

) f () g () g

A g

C -

().)

gC

,f( ()) .

x0

M

Cf

f(x0)=

=x+:

x0+

x0

M

Cf

f(x0 )

C

g(x0)=

Cf

C

A

B

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1. 2f(x) x x 3 0, 1 .

f

C .

2. 2f(x) ln x x 3 , , R : 2x y 4 0 -

fC A 1,f(1) .3. f

3 2 3 4f(x) x f(x) 2x 4x -

x . f

C A 1,f(1) .

4. f : 2xlnx f(x) x x x . -

0

x 1

f

C M 1,f(1) .

5. 2f(x) x x 1 . -

f

C :

) (1,1)

) (2,1) .

6. 2f(x) x 4x 33 , 2g(x) x 1 .

7. f 3 2f(x) x x 2x 5 () : 2x y 1 .

) ()

f .

) () f

C .

8. x 1f(x) x e 3 2g(x) x 3x 5x . -

f

C A 1,f(1) , gC .

9. 2f(x) 2x x 2g(x) x 4x 1 .

10. f y 2x 1 f

C

1 . 2

x 1

f (x) 1limx 1

.

11. 2f(x) x 2x 6 7 , .

) , f

.

) , f

C xx.