-
1
:
I- : : -)1 :01
: f
( ) ( ) 2 311 : f x xx
= +
) ) ( ) 3 312 : f x xx
= ) ) ( ) 3 213 : f x x
x= ) ) ( ) 2 2
14 : f x xx
= +
( ) ( )5 : 3. 2 2f x x x x= + ) + ) ( ) 26 : 2. 3 3f x x x x=
+
( ) ( )2
27 : 9xf x
x=
) ) ( )
3
28 : 2. 3xf x
x x=
+) ) ( ) 29 : 2. 3f x x x= +
:02 ): f ) 3 2f x x= + x
) - )f ( ), ,O i j. ) - )f x x x .
:03
): g )2 ; 1 0
3; 1x x
g xx x
= +
) - )g ( ), ,O i j. ) - )g x x x + .
: -)2
fD f :
fD fx x : f - D ) ) ( )f x f x =.
-
2
fD fx x : f - D ) ) ( )f x f x = .
: 0 f - fD :( )0 0f =.
) :01 )f f ( ), ,O i j ) f - )f ( )Oy .
) f - )f O .
II- : : -)1 ): f : ) 3 2 1f x x x= + +
) f )f x x .
:
D 0f fD D f -
): ) 0f x x fD.
0f fD D f - D
): ) 0f x .fD x
) :02 )f f ( ), ,O i j ) fD f - )f ( )Ox.
) fD f - )f ( )Ox.
:04
): f )2
2
6 56
x xf xx x +
= + +
) fD - )f x x fD.
) - )2
2
4 12 5: 02 3x xI
x x +
+ +
.
: -)2 gD fD g f :
-
3
f gD D D
f D g f - g D :
( ) 0f g .D
f D g f - g D :
( ) 0f g .D
: g f :
( )( )( )
3 2
2
3 2 11 :
1
f x x x x
g x x x
= +
= + ) ) ( )
( )
3 2
2
12 : 1
1
x xf xx
g x x
+ =
= +
:05
: ( )2
1,00000041,0000006
A ) = )20,9999995
0,9999998B =
: ( )2
1 4.:1 6.
xf xx
+
+
( )21 5.:1 2.
xg x
x
.
f - gD D D= .g f D
) - )710f ) )710g .B A
) D g f : 03 )f ( )g
) ), ,O i j ) D g f - )f ( )g .
:06
21 1: xf x
x+
) ) :2xD y =.
: -)3 :
): f )2
2
31
x xf xx
=+
-
4
) - )1 32 2
f x . x
. -
. m M fD f :
) M f - )f x M x fD.
) m f - )f x m x fD.
. f - :
.0 0
:04 [ f : +,0]
( )f x x fD.
) :50 )f f ( ), ,O i j ) M f - )f ( ) :D y M=.
) m f - )f ( )' :D y m=.
: g f :07
( ) 2 4xf x
x=
+) )
2
2
44
x xg xx
=+
.
) - ) 14
f x . x
g -
.
III- : : -)1
:2: :08 6f x x x + +:2: 4 12 5g x x x . +
: f :90
-
5
( )1 ; 1
3; 1 22 9; 2
x xf x x x
x x
= + +
) )f ( ), ,O i j f . : -)2
.fD 0x fD f:
0x I 0x f - I
) ) ( )0f x f x x I.
0x I 0x f - I
) ) ( )0f x f x x I.
IV- : : -)1 ): f : 10 ) 2 3f x x x= .
. + f - . f -
. f -
) : g :11 ) ( )3g x x x= .
. + g -
. g -
. g -
: -)2 :
fD I fD f
: I f -
( ) ( ) 0f x f y
x y
x I y x y.
: I f -
-
6
( ) ( ) 0f x f y
x y
x I y x y.
2ax - : bx c+ :a* +
ax - bcx d
++
c* :
V- : : -)1 :12
: g f
( ) 2 2 3f x x x= ) + ) 11
xg xx +
=+
.
) - )f ( )g.
) - )f ( )g ( ), ,O i j.
) - )3 23 2 2: 0
1x x xI
x+
+
.
f:3 -)3 x ax *a:
f: -)4 x x a :a
: -)5 fD I fD f:
) f I ){ }/f x x I ( )f I
) ) ( ){ }/f I f x x I= .
] : ]1,3I ] = ]1,1J = ] ]0, 2K =
f :( ) 2 2f x x x= .
] :13 [4, 3I = [ ]0, 4J 3 = 1,2 2
K =
): g )2
xg xx
=+
.
VI- : : -)1
-
7
J I g f :
) )f I J
: I h g f
( ) ( )( )h x g f x= x I h g f
: ( ) ( )( )
:gf
I Jg fx f x g f x
.
: g f :
( ) 2 2f x x x= ) + ) 2 2g x x x= .
g f f g f f g g.
g : f f g .
gD fD g f : -
): ){ }/g f f gD x D f x D =
: ( ) ( )( )
:
gf
g f gD Dg fx f x g f x
.
: g f :
( ) 2f x x x= ) + ) 6g x x=
g fD f gD g f f g .
: -)2 J I g f :06
) )f I J
J I g f -
g f I.
J I g f -
g f I.
) h f :14 ) 1f xx
) = ) 24 1xh x
x
=.
-
[email protected]
Prof : ABDELLAH BEN ELKHATIR Lyce ALFATH KHEMISSET
8
g: g - f h =.
[ h - ,10 0,]2
1 ,2 +
.
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