Sekantensteigungsfunktion
Author: Dörte Haftendorn
Date: 2 November 2013

Für das Fahrrad sorgte Prof. Dieter Riebesehl.

Sekantensteigungsfkt t

Ha 09/2013

Ableitung von f

um x0 verschobene Fkt t

h

deren stetige Fortsetzung

Ha 09

h

Bewege mit h Pfeiltasten

t(h)=\frac{(f(x_0+h)-f(x_0)}{h}

h = 1.75 (slider from -5 to 5, step 0.01)
x0 = 1 (slider from -2 to 4, step 0.1)
f(x) = x^(2) / 4 + 2
H: (x0 + h, f(x0 + h))
a_3 = OrthogonalLine(H, xAxis)
P: (x0, f(x0))
b_3 = OrthogonalLine(P, a_3)
J_1 = Intersect(a_3, b_3)
poly1, breit, hoch, j_3 = Polygon(P, J_1, H)
t(x) = (f(x0 + x) - f(x0)) / x
Fahrradgröße = 0.5 (slider from 0.2 to 1.2, step 0.1)
ny(x) = f(x) + (0.5 * Fahrradgröße / sqrt(1 + f'(x)^(2)))
nx(x) = x - ((0.5 * Fahrradgröße) * f'(x) / sqrt(1 + f'(x)^(2)))
e = Circle(P, (0.5 * Fahrradgröße))
a = Tangent(P, f)
c = OrthogonalLine(P, a)
C, D = Intersect(e, c)
M = If(y(D) > y(P), D, C)
P_1 = Root(sqrt((nx(x) - x(M))^(2) + (ny(x) - y(M))^(2)) - (1.3 * Fahrradgröße), x(P), x(P) + (2.5 * Fahrradgröße))
B: (x(P_1), f(x(P_1)))
g = Circle(B, (0.5 * Fahrradgröße))
b = Tangent(B, f)
d = OrthogonalLine(B, b)
E, F = Intersect(g, d)
N = If(y(F) > y(B), F, E)
G = Midpoint(M, N)
G' = Rotate(G, 60*°, M)
l = Segment(G', M)
m = Line(G, l)
i = Segment(M, G)
n = Line(G', i)
H_2 = Intersect(m, n)
a_1 = Ray(G, H_2)
h_4 = Circle(M, P)
k = Circle(N, B)
α = Angle(G, M, G')
p = Segment(G', H_2)
b_1 = Ray(G, G')
f_1(x) = sqrt((nx(x) - x(M))^(2) + (ny(x) - y(M))^(2)) - (1.3 * Fahrradgröße)
s = Circle(G, (0.8 * Fahrradgröße))
I = Intersect(s, b_1)
J = Intersect(s, a_1)
j = Segment(J, G)
q = Line(J, p)
c_1 = Circle(J, (0.2 * Fahrradgröße))
K, L_2 = Intersect(c_1, q)
d_1 = Segment(K, L_2)
e_1 = Circle(M, (0.1 * Fahrradgröße))
g_1 = Circle(G, (0.15 * Fahrradgröße))
h_1 = Ray(G, M)
k_1 = Circle(G, (1.95 * Fahrradgröße))
O = Intersect(k_1, h_1)
i_1, j_1 = Tangent(O, g_1)
Q, R = Intersect(e_1, j_1)
S, T = Intersect(e_1, i_1)
U = Intersect(g_1, i_1)
V = Intersect(g_1, j_1)
l_1 = Segment(Q, V)
m_1 = Segment(S, U)
H' = Rotate(H_2, 90*°, N)
H'_1 = Rotate(H_2, 260*°, N)
n_1 = Ray(N, H')
p_1 = Ray(N, H'_1)
q_1 = Circle(N, (0.53 * Fahrradgröße))
W = Intersect(q_1, n_1)
Z = Intersect(q_1, p_1)
r_1 = CircleArc(N, Z, W)
G'' = Rotate(G', 130*°, M)
β = Angle(G', M, G'')
G''_1 = Rotate(G', 280*°, M)
s_1 = Ray(M, G'')
t_1 = Ray(M, G''_1)
c_2 = Circle(M, (0.53 * Fahrradgröße))
A_1 = Intersect(c_2, s_1)
B_1 = Intersect(c_2, t_1)
d_2 = CircleArc(M, B_1, A_1)
G''_2 = Rotate(G', (-4 * x(P)), G)
γ = Angle(G', G, G''_2)
a_2 = Line(G''_2, G)
e_2 = Circle(G, (0.2 * Fahrradgröße))
C_1, D_1 = Intersect(e_2, a_2)
b_2 = Segment(D_1, C_1)
f_2 = Line(C_1, i)
g_2 = Line(D_1, i)
h_2 = Circle(C_1, (0.05 * Fahrradgröße))
E_1, F_1 = Intersect(h_2, f_2)
i_2 = Segment(E_1, F_1)
k_2 = Circle(D_1, (0.05 * Fahrradgröße))
p_2(x) = 3 - (x - 6)^(2) / 12 - (x - 6)^(3) / 54 + (2 * sin(x))
s_2(x) = (x - 1)^(2) / 5 + 1
Sekante = Line(P, H)
f_3(x) = f'(x)
m_sH: (x(H), (y(H) - y(P)) / (x(H) - x(P)))
h_3 = OrthogonalLine(P, xAxis)
L: (x0, 0)
n_2 = Segment(P, L)
steig: hoch / breit
o = false
v = false
msek = Vector((x0, 0), (x0, 1))
r(x) = t(x - x0)
H_1: (h, t(h))
t_s(x) = If[x ≠ 0, t(x),f_3]
A: (0, f_3(x0))
G_1: (x0, f_3(x0))
z = Vector(A, G_1)
o_1 = false
hv = Vector((x0, 0), (x(H), 0))
u: t(2)
w = false
H1 = NaN
u_1 = Vector((h, 0))
v_1 = Vector((h, 0), (h, y(m_sH)))
w_1 = Vector((x(H), 0), (x(H), y(m_sH)))
Text5: "f(x)=" + (LaTeX[f]) + ""