signe \ de \ \textit{ f'(x)}

variation \ de \ \textit{f}

f(x)=

x

Fonction dérivée

Tableau rempli

Tracer fonction

A = (0.07444899886724571, -3.6481853117054377)
c = Line(A, y = 0)
d = OrthogonalLine(A, c)
C = Point(d)
k = OrthogonalLine(C, d)
P = Point(k)
f(x) = (2 * x) - 3
f' = Derivative(f, x)
h(x) = sgn(f'(x))
n = Dimension(liste1)
liste2 = Sequence(x(Element[liste1, i]), i, 1, n)
liste3 = Sequence((Element[liste2, i] + Element[liste2, i + 1]) / 2, i, 1, n - 1)
liste4 = Append(Element[liste2, 1] - 1, liste3)
liste5 = Append(liste4, Element[liste2, n] + 1)
liste6: h(liste5)
a: h(2.64)
b: h(0)
B = Point(d)
e = OrthogonalLine(B, d)
D = Point(k)
j = OrthogonalLine(D, k)
E = Intersect(e, j)
F = Intersect(c, j)
liste7 = Sequence(Translate[B, Vector[(i / (n + 1) * Vector[B, E])]], i, 0, n + 1)
liste8 = Sequence(Translate[A, Vector[(i / (n + 1) * Vector[B, E])]], i, 0, n + 1)
liste10 = Sequence(Vector[If[Element[liste6, i]  <  0, Vector[Element[liste7, i], Element[liste8, i + 1]], Vector[Element[liste8, i], Element[liste7, i + 1]]]], i, 1, n + 1)
ChampTexte1 = Textfield(f)
r: Distance[C, D] / ((6 * n))
liste9 = Sequence(Translate[C, Vector[(i / (n + 1) * Vector[B, E])]], i, 0, n + 1)
liste11 = Sequence(Midpoint[Segment[Element[liste7, i], Element[liste9, i + 1]]], i, 1, n + 1)
L = (1.4546758375639424, 3.3679677850027825)
G = (15.97059689033574, 7.027340344062839)
i1 = Line(G, y = 0)
p = Circle(G, r)
l = OrthogonalLine(G, i1)
H = Intersect(p, l, 2)
I = Intersect(p, l, 1)
J = Intersect(p, i1, 2)
K = Intersect(p, i1, 1)
m = Segment(K, J)
q = Segment(H, I)
liste12 = Sequence(TH[r, Element[liste11, i]], i, 1, n + 1)
M = Midpoint(C, P)
i2 = OrthogonalLine(M, k)
N = Intersect(e, i2)
O = Midpoint(M, N)
s = OrthogonalLine(P, k)
Q = Intersect(c, s)
S = Intersect(e, s)
R = Midpoint(S, A)
T = Point(d)
t = OrthogonalLine(T, d)
U = Intersect(j, t)
liste14 = Sequence(Translate[T, Vector[(i / (n + 1) * Vector[B, E])]], i, 0, n + 1)
V = Midpoint(T, C)
liste15 = Sequence(Translate[V, Vector[(i / (n + 1) * Vector[B, E])]], i, 0, n + 1)
W = Intersect(s, t)
texte3 = Text(-Infinity, V + (0.2, 0))
Z = Intersect(e, s)
i4 = Segment(W, U)
b_1 = Segment(W, Q)
c_1 = Segment(Q, F)
e_1 = Segment(Z, E)
f_1 = Segment(P, D)
k_1 = 0
liste18 = Sequence(If[Element[liste6, i] > 0, TV[(7 * Distance[C, B] / 20), Element[liste11, i]]], i, 1, n + 1)
liste16 = Sequence(Text[Element[liste2, i], Element[liste15, i + 1]], i, 1, n)
a_1 = Segment(T, A)
d_1 = Segment(U, F)
A_1 = Midpoint(C, B)
liste13 = Sequence(Translate[A_1, Vector[(i / (n + 1) * Vector[B, E])]], i, 0, n + 1)
liste19 = Sequence(Circle[Element[liste13, i], (3 * Distance[C, B] / 20)], i, 2, n + 1)
B_1 = Midpoint(Element[liste13, 1], Element[liste13, 2])
g_1 = TV((7 / 20 * Distance[C, B]), B_1)
i = TH((4 / 20 * Distance[C, D]), B_1)
liste20 = Sequence(Text["0", (x(Element[liste13, i]) - 0.1, y(Element[liste13, i]))], i, 2, n + 1)
liste17 = Sequence(Segment[Element[liste9, i], Element[liste7, i]], i, 2, n + 1)
C_1 = Midpoint(W, C)
o = false
texte5: "\textit{f'(x) = " + (LaTeX[f']) + "}"
g = false
u = false
texte4 = Text("+∞", Element[liste15, n + 2] - (1, 0))

Tool: TH
TH[ <Nombre>, <Point> ]
Input: r, G
Output: m

i = Line(G, y = 0)
p = Circle(G, r)
J = Intersect(p, i, 2)
K = Intersect(p, i, 1)
m = Segment(K, J)

Tool: TV
Input: r, G
Output: q

i = Line(G, y = 0)
p = Circle(G, r)
l = OrthogonalLine(G, i)
H = Intersect(p, l, 2)
I = Intersect(p, l, 1)
q = Segment(H, I)