Inéquation produit.

♥
f[−10; 10] x∈[−10; 10]
f(x) = (3x−7)x2(−x+ 1)
g:[−6; 4] →R
x7→ (x+ 4)(−x+ 2)
−2(x+ 1)(−7−x)≥0R
(x−5)(−2x+ 6) ≥0
(3x−5)(x+ 4) >0
(x+ 3)(−x+ 6) ≤0
(−x+ 4)(3x+ 2) >0
(10x+ 5)(−3x+ 4) >0
(x−4)(3 −x)≤0
(−2x+ 3)(5 + x)>0
3x(3x−5) <0
−(x+ 1)2(2x−1) ≥0
−2x(x−1)(4 −x)≤0
x2(4 −x)(−2x+ 1) >0
x3(x+ 1) <0
(x2+ 1)(x−1) ≥0
(x−2)(4 −x)<0
3
4−x x−7 6≥0
(x+√3)(x−4) ≥0
(3x−7)(7 −3x)≤0

(2x−4)(x+ 5) + x > −5 (2x−3)(x+ 5) >0
(2x−4)(x+ 5) + x > −5
Rx2≤16
x2−4x≤ −2x−1
3x(x+ 3) −(x+ 3)2≤0
x3+ 2x2+x≥0
x(x+ 6) >3(x+ 6)
2x(x−3) + 3x−9<6x−18
x2(1 −3x) + 4(6x−2) ≥0
(1 −2x)x−4x(x+ 6) ≤0
7−2x2= 2x−2√7
(x2−1) + 2x−2=6x−6
x2≤10
x2≤ −16
x2≤0
x2<8
x2≤144
x2≤20
x2+4+(x+ 2)(2x+ 5) <0
(x+ 1)(x−3) ≥x2−9
4x−4+(x−1)(x−4) + x2−1>0
(x+ 5)2≤(x+ 5)(x+ 3)
(2x−1)(x+ 3) ≥x−1
2(x+ 6)
−x+1
−2x+8 >0
R

2x−4
x+2 ≤0
−2x+8
3x−2≤0
2x+4
x−1−2≥0
2x+4
x+1 <3
2x+3
x+1 ≤x−6 x+1
1<2x+10
−x+3
x+3
2x−1≥0
2−x
5−2x≤0
3x−1
−x+5 >0
5x(x−2)
4x+1 <0
2x2
(−x+1)(x+3) ≥
−x(x−4)
2+x2≤0
(x+1)(x−2)
3−x>0
9−4x
11−5x<0
−5+4x
2x−1≥0
x+1
3−x≤0
7−2x
2x−1>0
−5x
(2x−7)2<0
1+2x2
7−x≥0
x+4
5−x<2
2x > 7x−1
−4x−10 ≥2−4x
2x2<2(x−7)2
x2<25
(x+ 3)2<−1
(x−6)2>16
(2x−√3)(2x+ 6) >0
36−12x
x−3≤0
x2−5<(x+√5)(x−2)
x2−25 + (x−5)(6 −x)≤0
2x+3
x−1≥4
q
C(q) = 0,02q2+ 0,1q+ 9
q∈[0; 80]
q
R(q) = 1,2q

q
B(q) = −0,02q2+ 1,1q−9
B(q) = −0,02(x−45)(x−10) q∈[0; 80]
q C(q)=2q2+ 10q+ 900
0< q < 80
R(q) = 120q
B(q) = −2(q2−55q+ 450)
B(q)B(q) = −2(q−10)(q−45)
f(x)
x
0≤x≤11 f(x) = x3−12x2+ 50x
30 000 eg(x)
B(x)B(x) = g(x)−f(x)
g(x)x
B(X)
(x−2)(x−10)
B(x)>0
f g R
f(x) = x2g(x)=2x+ 1
x f(x)−g(x)=(x−1−√2)(x−1 + √2)
f(x)< g(x)

x[0; 8]
4 cm xcm
x
4
x
πx2
8≤2x
[0; 8]
0; 16
π
ABCD x cm
x > 6E[AB]
EB = 6 cm
x
cm2AED
x
ABCD
AED
A B
CD
E
//
//
x
ABC A
AB = 8 AC = 6 M
[BC]
M(AB)
(AC) [AB] [AC]
P Q
BM =x
AP MQ A B
C
M
P
Q
x
MP = 0,6x MQ = 8 −0,8x
x p(x)AP MQ
M13,5