Croissance
Author: Daniel Mentrard

Déplacez le point A

Para modificar el valor de cada parámetro, 

desliza los puntos verdes o bien pulsa + o - tras 

seleccionar el parámetro en la ventana de la izquierda 

x

f '(x)

f(x)

+

-

0

+

-

Tableau de variation sur 

t = -3.2 (slider from -10 to 10, step 0.01)
a = 0.5 (slider from -2 to 2, step 0.1)
b = 1.5 (slider from -10 to 10, step 0.5)
c = 3 (slider from -50 to 50, step 0.5)
f(x) = a * x^(2) + b * x + c
A: (t, f(t))
b_1 = Tangent(A, f)
c_1 = OrthogonalLine(A, yAxis)
a_2 = 6.499999999999998 (slider from -5 to 10, step 0.1)
d = Circle(A, a_2)
B, C = Intersect(d, b_1)
e = Segment(B, C)
g = Segment(A, (x(A), 0))
A_1: (-9.03, -10 + 18 * sgn(f'(x(A))))
A_2: (-8, 8 + 20 * sgn(f'(x(A))))
A_3: (-9, 28 + 20 * sgn(f'(x(A))))
Q: (x(A) + 1, y(A))
h = OrthogonalLine(Q, xAxis)
R = Intersect(h, b_1)
S, r, p, q = Polygon(A, Q, R)
D = (-1, 6)
F = (-1, 10)
F_1 = (2, 9.6)
E = (2, 6.2)
G = (-10.8, 9.6)
H = (-10.8, 6.2)
I: (x(E), y(E))
J: (x(F_1), y(F_1))
K = (-7.73, 5.5)
L = (-4, 6.4)
M = (-15.88465350367789, 4.590217972611615)
coef: (y(C) - y(B)) / (x(C) - x(B))
N = (-15.800289369671102, 6.61495718877454)
O = (-17, 7)
P = (-9, 7)
T = (-9, 3)
U = (-17, 3)
V = (-17.06575137977293, -1.4839996758771616)
W = (-11.033715798287547, -1.526181742880556)
Z = (-11, -7)
A1 = (-17, -7)
B1 = (-17, 12)
C1 = (-9, 12)
D1 = (-9, 9)
E1 = (-17, 9)
F1: (x(A), 0)
T15: "x_0 = " + (x(A))
Mini: (-b) / (2 * a)
T16: "x_0 = " + (x(A))
G1 = (-7.9544249070397655, 6.741503389784723)
H1 = (-4, 3)
I1 = (-8, 3)
J1 = (-4, 7)
L1 = (-3, 7)
M1 = (-3, 3)
T6: "" + Mini
Inf: Mini - 10
T9: "" + Inf
Sup: Mini + 5
T10: "" + (Sup + 5)
aff = If(t ≥ Mini - 10, 1, 0)
K1 = (-28, 10)
N1 = (-23.130984247989986, 6.11315931970216)
u = Vector(K1, N1)
O1 = (-20.877113376369643, 6.051040301074107)
P1 = (-16, 10)
v = Vector(O1, P1)
T18: "[ " + (Mini - 10) + " ;" + (Sup + 5) + " ]"
affigauche = If(t ≥ Mini - 10, If[coef ≤ 0, If[t ≥ Mini, 3, 2], If[t ≥ Mini, 2, 3]], 0)
Q1 = (-28, 6)
R1 = (-23, 10)
w = Vector(Q1, R1)
affidroite = If(t ≥ Mini, If[coef ≤ 0, If[t ≥ Mini, 3, 2], If[t ≥ Mini, 2, 3]], 0)
S1 = (-21, 10)
U1 = (-15.985342097614994, 5.857957814331625)
z = Vector(S1, U1)
V1 = (-32, 14)
W1 = (-14, 14)
Z1 = (-14, 5)
A2 = (-32, 5)
poly1, v1, w1, z1, a2 = Polygon(V1, W1, Z1, A2)
B2 = Point(a2)
C2 = Point(w1)
i = Segment(B2, C2)
D2 = Point(v1)
E2 = Point(z1)
j = Segment(D2, E2)
F2 = Point(a2)
G2 = Point(w1)
k = Segment(F2, G2)
T19: "" + (f(Mini))
editmini = If(t ≥ Mini, If[f(Mini) ≤ 0, 1, 2], 0)
T20: "" + (f(Mini))