Nombre dérivé
Author: Yvan Monka - m@ths et tiques 2013

f(x)=

a+h

a

f(a+h)

f(a)

h

f(a+h)-f(a)

h = 0.43 (slider from 0 to 2, step 0.01)
f(x) = x^(3) - 2 * x^(2) - 1.84
a = 1.7 (slider from -10 to 10, step 0.1)
ChampTexte1 = Textfield(f)
A: (a, f(a))
M: (a + h, f(a + h))
a_1 = Line(A, M)
b = OrthogonalLine(A, xAxis)
c = OrthogonalLine(M, xAxis)
d = OrthogonalLine(M, yAxis)
e = OrthogonalLine(A, yAxis)
C = Intersect(c, xAxis)
D = Intersect(b, xAxis)
E = Intersect(d, yAxis)
F = Intersect(e, yAxis)
g = Segment(M, C)
i = Segment(M, E)
j = Segment(A, D)
k = Segment(A, F)
l = OrthogonalLine(A, yAxis)
m = OrthogonalLine(M, l)
B = Intersect(l, m)
u = Vector(A, B)
v = Vector(B, M)
n = Tangent(A, f)
G = Intersect(xAxis, yAxis)
p = Segment(E, G)
q = Segment(G, F)
texte1: "$ \frac{f(a+h)-f(a)}{h}=\frac{" + (LaTeX[y(M)]) + "-" + (LaTeX[y(A)]) + "}{" + (LaTeX[h]) + "}=" + (LaTeX[(y(M) - y(A)) / h]) + " $"