Von der Sekanten- zur Tangentensteigung
Author: Aarnds

Q

P

Differenzenquotient:

Tangente

m_1=1

Sekante

Intervallänge = 7 (slider from 0 to 7, step 0.1)
f(x) = -(0.1) * (x - 8.0)^(2.0) + 7.5
B: (3.0 + Intervallänge, f(3.0 + Intervallänge))
A = Point(f)
a: (x(A), 0.0)
b: (x(B), 0.0)
C: (x(B), y(A))
Vieleck1, b_1, a_2, c = Polygon(A, C, B)
D = Midpoint(A, C)
E = Midpoint(a_2)
d = Segment(a, b)
F: (0.0, y(A))
G: (0.0, y(B))
e = Segment(F, G)
g = Segment(G, B)
H = Intersect(a_2, b_1)
i = Segment(H, b)
j = Segment(A, a)
h = Segment(A, F)
k = Tangent(A, f)
a_1 = Line(A, B)
m_1 = Slope(a_1)
m = Slope(k)
Text8: " \frac{ f(x_0+h)-f(x_0) }{ h }= \frac{" + (y(B) - y(A)) + "}{" + (x(B) - x(A)) + "}\;=\;" + m_1
Text5: "f(x_0+h)=" + (y(B))
Text6: "f(x_0)=" + (y(A))
Text1: "x_0=" + (x(A))
Text2: "x_0+h=" + (x(B))
Text4: "f(x_0+h)-f(x_0)=" + (y(B) - y(A))
Text3: "h=" + (x(B) - x(A))