fonctionimpaire
Author: mp
Date: 25/04/2005

-4.5

1.79

 4

x

f(x)

Tableau de variations

-4.5

-4

-3

-2

-1

0

1

2

3

4

x

y

y

x

Tableau de valeurs (points x sur la courbe)

1

1

Représentation graphique

Modifier la valeur de x

Derive f'

Function f

Domain

+

-

+

f'(x)

0

0

is positive

is negative

-4.5

f(x) = 0.2 * (x + 0.04)^(3) - 2 * (x + 0.04) - 0.04
c = 4 (slider from -4.5 to 4, step 0.01)
M: (c, f(c))
P: (0, y(M))
N: (c, 0)
a = Segment(N, M)
b = Segment(M, P)
T2: x(M) + ""
T3: "f(" + (x(M)) + ")=" + (y(M))
I = (7, 1.5)
J = (9.054943771848599, 4.397607964331198)
K = (9.997245577331437, 4.397607964331198)
O = (13.49288130734842, 1.5707025478826833)
Q = (15.590262745358608, 4.5191952940709195)
w = Vector(I, J)
R = (12.5, 1.5)
z = Vector(K, R)
e = Vector(O, Q)
f1 = Function(f, -4.5, 4)
T4: "" + (f(-4.5))
T8: "" + (f(1.8))
T9: "" + (f(4))
A = (6.303968324349302, 5.712777827044512)
B = (16.803968324349302, 5.712777827044512)
d = Segment(A, B)
C = (6, 6.5)
D = (16.773571491914375, 6.5)
E = (16.773571491914375, 0.5)
F = (6, 0.5)
G = (4.343434744434412, 0.49189393198868814)
H = (4.343434744434412, 5.73506859146813)
L = (4.343434744434412, 6.491893931988688)
poly1, l, d_1, e_1, g = Polygon(L, D, E, G)
h = Segment(C, F)
i = Segment(H, A)
S = Intersect(xAxis, yAxis)
j = Segment(S, N)
k = Segment(S, P)
T13: " x = " + c
T = (4.5, -3.5)
T26: "" + (f(-4.5))
T27: "" + (f(-4))
T28: "" + (f(-3))
T29: "" + (f(-2))
T30: "" + (f(-1))
T31: "" + (f(0))
T32: "" + (f(1))
T33: "" + (f(2))
T34: "" + (f(3))
T35: "" + (f(4))
U = (20.5, -3.5)
m = Segment(T, U)
V = (4.5, -5.5)
W = (20.5, -5.5)
n = Segment(V, W)
p = Segment(T, V)
Z = Point(m)
A1 = Point(n)
q = Segment(Z, A1)
B1 = Point(m)
C1 = Point(n)
r = Segment(B1, C1)
D1 = Point(m)
E1 = Point(n)
s = Segment(D1, E1)
F1 = Point(m)
G1 = Point(n)
t = Segment(F1, G1)
H1 = Point(m)
I1 = Point(n)
a1 = Segment(H1, I1)
J1 = Point(m)
K1 = Point(n)
b1 = Segment(J1, K1)
L1 = Point(m)
M1 = Point(n)
c1 = Segment(L1, M1)
N1 = Point(m)
O1 = Point(n)
d1 = Segment(N1, O1)
P1 = Point(m)
Q1 = Point(n)
e1 = Segment(P1, Q1)
R1 = Point(m)
S1 = Point(n)
g1 = Segment(R1, S1)
U1 = (21, -3.5)
V1 = (21, -5.5)
h1 = Segment(U1, V1)
i1 = Segment(U, U1)
j1 = Segment(V1, W)
W1 = Point(p)
Z1 = Point(h1)
k1 = Segment(W1, Z1)
A2 = Point(xAxis)
B2 = Point(xAxis)
C2 = Point(yAxis)
D2 = Point(yAxis)
l1 = Segment(A2, B2)
m1 = Segment(C2, D2)
E2 = Point(l1)
F2 = Point(m1)
f'(x) = f'(x)
f_1 = If(f'(x) < 0, f')
A_1 = Point(g)
B_1 = Point(d_1)
a_1 = Segment(A_1, B_1)
b_1 = Tangent(M, f1)
c_1 = Circle(M, 2)
C_1, D_1 = Intersect(c_1, b_1)
g_1 = Segment(C_1, D_1)
o = Slope(b_1)
E_1 = (4.182641079564552, 7.95403735921804)
F_1 = (4.282641079564551, -3.900727290404765)
h_1 = Line(E_1, F_1)
G_1 = Max(f, -4, 5)
H_1 = Min(f, -4, 5)
i_1 = Segment((-4.5, 0), (4, 0))
j_1 = Segment(G_1, (x(G_1), 0))
p_1 = Function(f, -4.5, c)
q_1 = Function(f', -4.5, c)
r_1 = Function(f_1, -4.5, c)
I_1 = Point(l)
J_1 = Point(e_1)
k_1 = Segment(I_1, J_1)
K_1 = (-4.684424488739881, 5.1575287752044545)
L_1 = Point(q_1)
M_1 = (-4.5020434941303, 0.7195912397046371)
N_1 = (-3.8941068454316943, -0.1011232360384797)
v = Vector(M_1, N_1)
O_1 = (-5.201170640133696, -7.24437885824709)
P_1: (-4.25, f(-4.25))
u_1 = Vector(O_1, P_1)
Q_1 = (-3.8333131805618335, 6.0086400833825016)
u = Vector(K_1, Q_1)
l_1 = Segment(H_1, (x(H_1), 0))
R_1 = Point(l)
S_1 = Point(e_1)
m_1 = Segment(R_1, S_1)
T6: "" + (f(x(G_1))) + ""
"" + (f(-2)): "" + (f(x(G_1))) + ""
T1: "" + (x(G_1)) + ""
texte10: "    f' (" + c + ") = " + (f'(c)) + "
or tangente coefficient
or pente"
texte13: "for  x = " + c + " ; y = f(" + c + ") =  " + (f(c)) + ""
liste1 = Sequence((i, f(i)), i, -4, 4)
liste2 = Take(liste1, 1, round(c) + 5)