180 / 1400 = 0,..
Soit : ..,.. %
520 / 1400 = 0,..
Soit : ..,.. %
370 / 1400 ...
330 / 1400 ...
Inscrits :
180 / 2500 = ...
520 / 2500 ...
370 / 2500 ...
330 / 2500 ...
Exercice III :
f(x) = -x^2 + 5x - 4
a) dérivée :
f'(x) = -2x + 5
Étudier son signe :
-2x + 5 = 0
2x = 5
x = 5/2
X...............|...-2....................5/2.....................6
-----------------------------------------------------------
-2x + 5....|...............(+).............O......(-)..............
b) tableau de variation :
f(-2) = -(-2)^2 + 5 * (-2) - 4
f(-2) = -4 - 10 - 4
f(-2) = (-18)
f(5/2) = -(5/2)^2 + 5 * (5/2) - 4
f(5/2) = -25/4 + 25/2 - 4
f(5/2) = -25/4 + 50/4 - 16/4
f(5/2) = 9/4
f(6) = -(6)^2 + 5 * 6 - 4
f(6) = -36 + 30 - 4
f(6) = (-10)
X...............|...-2....................5/2.....................6
-----------------------------------------------------------
-2x + 5....|...............(+)......... O......(-)..............
f(x)...........|.flèche monte...9/4.flèche descend
f(x) = 0
-x^2 + 5x - 4 = 0
(Delta)^2 = (5)^2 - 4 * (-1) * (-4)
(Delta)^2 = 25 - 16 = 9
Delta = V9
Delta = 3 > 0 donc deux solutions
X1 = (-5 - 3) / (2 * -1)
X1 = (-8) / (-2)
X1 = 4
X2 = (-5 + 3) / (2 * -1)
X2 = (-2) / (-2)
X2 = 1
f(x) = (x - 4)(x - 1)
X...............|...-2............1...............4.....................6
-----------------------------------------------------------
x - 4.........|...............(-).................O........(+).........
x - 1..........|.......(-)........O...............(+)...................
f(x)...........|........(+)......O....(-).......O........(+).........
