Exercice 1 :
f(x) = 8x^2 - 5x
1)a) image de (-1) :
f(-1) = 8 * (-1)^2 - 5 * (-1)
f(-1) = 8 + 5
f(-1) = 13
b) f(1/3) :
f(1/3) = 8 * (1/3)^2 - 5 * (1/3)
f(1/3) = 8 * (1/9) - 5/3
f(1/3) = 8/9 - 5/3
f(1/3) = 8/9 - 15/9
f(1/3) = (-7/9)
2)a) f(3) = 57 ?
f(3) = 8 * (3)^2 - 5 * 3
f(3) = 8 * 9 - 15
f(3) = 72 - 15
f(3) = 57
b) antécédent de 0 :
f(x) = 0
8x^2 - 5x = 0
x(8x - 5) = 0
x = 0 et 8x - 5 = 0
x = 0 et 8x = 5
x = 0 et x = 5/8
Exercice 2 :
a) A(x) = (x + 5)x + (2x - 3)(x + 5)
A = (x + 5)(x + 2x - 3)
A = (x + 5)(3x - 3)
A = (x + 5) * 3(x - 1)
A = 3(x + 5)(x - 1)
A = B
b) A(x) = (2x - 1)(3x - 5)
B(x) = (2x - 1)^2 - (4 - x)(2x - 1)
B = (2x - 1)(2x - 1 - 4 + x)
B = (2x - 1)(3x - 5)
A = B
c) A(x) = [(x + 1)(x + 2)] / x
A = (x^2 + 2x + x + 2) / x
A = (x^2 + 3x + 2) / x
A = x + 3 + 2/x
A = x + 2/x + 3
A = B
Exercice 3 :
a) diamètre = x
d + h = 10
x + h = 10
h = 10 - x
b) volume = Pi * r^2 * h
V = Pi * (x/2)^2 * (10 - x)
c) je n'ai pas de calculatrice
Exercice 4 :
f(x) = -4x^2 + 16x + 50
x = - 3
f(x) = -4 * (-3)^2 + 16 * (-3) + 50
f(x) = -4 * 9 - 48 + 50
f(x) = -36 + 2 = (-34)
x = -2
f(x) = -4 * (-2)^2 + 16 * (-2) + 50
f(x) = -4 * 4 - 32 + 50
f(x) = -16 + 18 = 2
x = -1
f(x) = -4 * (-1)^2 + 16 * (-1) + 50
f(x) = -4 * 1 - 16 + 50
f(x) = -4 + 34 = 32
x = 0
f(x) = -4 * (0)^2 + 16 * (0) + 50
f(x) = -4 * 0 - 0 + 50
f(x) = 50
x = 1
f(x) = -4 * (1)^2 + 16 * (1) + 50
f(x) = -4 * 1 + 16 + 50
f(x) = -4 + 66 = 62
x = 2
f(x) = -4 * (2)^2 + 16 * (2) + 50
f(x) = -4 * 4 + 32 + 50
f(x) = -16 + 82 = 66
x = 3
f(x) = -4 * (3)^2 + 16 * (3) + 50
f(x) = -4 * 9 + 48 + 50
f(x) = -36 + 98 = 62
x = 4
f(x) = -4 * (4)^2 + 16 * (4) + 50
f(x) = -4 * 16 + 64 + 50
f(x) = -64 + 114 = 50
