Sujet - matheclair
!"
Ex1 :#$%
z1=−5+2 i
z2=3−i
&
''(')*+'#détailler les calculs%
,-''''&
z1+z2
.
'
/
0','
''
z2−z1
.
'
/
0','
''
z1
2
.
'
/
0','
''
z1×z2
.
'
/
0','
''
z1
z2
.
'
/
0','
''
1
iz2
.
'
/
0','
''
Ex2 :#1%2*'
%
f
('
'&
'%'*'-*'
y=6x−17
''),''-'3&
4
f ' (3)
&
%'*'-*'
y=2,5
'
'),''-'&
4
f ' (1)
&
%25''),'
6'-'7)',
81&'&
Ex3 :#9%
%'% ''('(
f
:ℝ '
f(x)=−4x3+x2−7x+1
%2'
Cf
'(
f
'6
')+;'<0<
%''('(
g
:=>?@A'
g(x)= 3x2+1
x−2
Ex4 :#1%
f
'(:=7>9A'
f(x)=2,5 x2+1
x
0'(
f '
*
f ' (x)=5x−1
x2
&
*'''),'
f
'"-'&
,-'''' 2-*' /
!B
Ex1 :#$%
z1=5−2 i
z2=−3+i
&
''(')*+'#détailler les calculs%
,-''''&
z1+z2
.
'
/
0','
''
z2−z1
.
'
/
0','
''
z1
2
.
'
/
0','
''
z1×z2
.
'
/
0','
''
z1
z2
.
'
/
0','
''
1
iz2
.
'
/
0','
''
Ex2 :#1%2*'
%
f
('
'&
'%'*'-*'
y=2x−7
''),''-'9&
4
f ' (5)
&
%'*'-*'
y=1,5
'
'),''-'&
4
f ' (2)
&
%25''),'
6'-'7)',
1&'&
Ex3 :#9%
%'%''('(
f
:ℝ '
f(x)=−2x3+x2−5x+3
%2'
Cf
'(
f
'6
')+;'<0<
%''('(
g
:
]3;+∞[
'
g(x)= 5x2+1
x−3
Ex4 :#1%
f
'(:=7>9A'
f(x)=1,5 x2+1
x
0'(
f '
*
f ' (x)=3x−1
x2
&
*'''),'
f
'"-'&
,-'''' 2-*' /
!"')#909%
Ex1 :#909%
z1=−5+2 i
z2=3−i
&
''(')*+'#détailler les calculs%
,-''''&
z1+z2
.
'
/
0','
''
z2−z1
.
z1
2
.
'
/
0','
''
z1×z2
.
'
/
0','''
z1
z2
.
'
/
0','''
Ex2 :#09%2*'
%
f
('
'&
'%'*'-*'
y=6x−17
''),''-'3&
4
f ' (3)
&
%25''),'
6'-'7)',
81&'&
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