50

P(x_0,f(x_0))

Q(x_0+h|f(x_0+h))

30

Start

Init

30

50

benötigte Zeit:

zurückgelegter Weg:

mittlere Geschwindigkeit:

B

Werkzeug einblenden

x_0 =

h =

f(x) = If[0 ≤ x ≤ 16, (-21 / 2560 * x^(4)) + (147 / 640 * x^(3)) - (63 / 40 * x^(2)) + (10 * x)]
x0: 12
y0: f(x0)
P: (x0 | y0)
h: 1
y1: f(x0 + h)
Q: (x0 + h | y1)
R: (x(Q) | y(P))
t = 0 (slider from 0 to 16, step 0.1)
v = Vector(R, Q)
Z0: (-2.4 | 0)
Z1: (-1.2 | 0)
Z2: (-1.2 | 40)
Z3: (-2.4 | 40)
h1 = Segment(Z1, Z2)
m: (y(Q) - y(P)) / (x(Q) - x(P))
Text1: "" + m + ""
A: (t | f(t))
HLA: (-2 | y(A) - 5)
HRA: HLA + (0.5 | 0)
VLA: HLA + (0 | 10)
vPQ: (y(Q) - y(P)) / (x(Q) - x(P))
vPQkmh: (vPQ * 3.6)
vAmax: (f'(12) * 3.6)
Z4: (-1.2 | 160)
v1, g, h2, k, l = Polygon(Z0, Z1, Z2, Z3)
Z5: (-2.4 | 160)
Z6: (-2 | 160)
v2, n, p, q, r = Polygon(Z2, Z4, Z5, Z3)
f2(x) = f''(x)
l1 = NSolve(f2(x) = 0)
Text3: " " + vAmax + " [km/h]"
u = Vector(P, R)
i = Segment(P, Q)
dx: x(Q) - x(P)
dy: y(Q) - y(P)
Text4: "" + dx + " [s]"
Text5: "" + dy + " [m]"
Text2: "\overline{v}_{PQ} = " + (LaTeX[vPQ]) + " [m/s ] \widehat{=} " + (LaTeX[vPQkmh]) + " [km/h]"
j = Line(P, Q)
B0: (12 | f(12))
B: (-1 | f(12))
Text9: "" + dx + ""
Text10: "" + dy + ""
bWerkzeug = false
Eingabefeld1 = Textfield(x0)
Eingabefeld2 = Textfield(h)
Text11: "f(x_0) = " + y0 + ""
Text12: "f(x_0+h) = " + y1 + ""