x

f(x)=

xMin =

xMax

dx

+

–

◦

x_0 =

mittlere Änderungsrate:
Steigung der Sekante:

Sekante

lokale Änderungsrate:
Steigung im Punkt:

\downarrow

h \rightarrow 0

\dots

xmax = 2 (slider from -5 to 10, step 0.1)
xmin = -2 (slider from -5 to 5, step 0.1)
dx = 1 (slider from -5 to 5, step 0.1)
f(x) = x^(2)
W = Sequence(f(i), i, xmin, xmax, dx)
H = Sequence(If[Element[W, i] ∈ {Infinity, -Infinity}, NaN, Element[W, i]], i, 1, Length[W])
W0 = Remove(W, {Infinity})
W2 = RemoveUndefined(H)
ymin0 = Min(W2)
ymax0 = Max(W2)
bMax = Max({abs(ymax0), abs(ymin0)})
P = Point(f)
x0: x(P)
h = 1 (slider from -5 to 5, step 0.1)
df: f(x0 + h) - f(x0)
a = 1
WT = Sequence({i, f(i)}, i, xmin, xmax, dx)
P0: (a | f(a))
Text1: "f: " + (LaTeX[a]) + " \rightarrow " + (LaTeX[f(a)]) + ""
pos = If(a < 0, ((xmax - xmin) / 15 | 0), Vector[(-((xmin - xmax) / 100 | 0))])
WText = Insert({{"x", "f(x)"}}, WT, 1)
Text2 = TableText(WText, "v|_ll")
b = 1 (slider from xmin to xmax, step dx)
ma = 1 (slider from -5 to 5, step 0.1)
ymax = If(ymax0 < 0, bMax / 10, ymax0 + bMax / 10)
ymin = If(ymin0 > 0, ((-bMax)) / 10, ymin0 - bMax / 10)
Eingabefeld1 = Textfield(f)
Eingabefeld2 = Textfield(xmin)
Eingabefeld3 = Textfield(xmax)
Eingabefeld4 = Textfield(dx)
W1 = RemoveUndefined(W0)
Q: (x0 + h | f(x0 + h))
s = Line(P, Q)
t(x) = (f'(x0) * (x - x0)) + f(x0)
m = Slope(s)
Eingabefeld5 = Textfield(x0)
v: (ymax - ymin + 2) / (xmax - xmin + 2)
R: (x(Q) | y(P))
u = Vector(P, R)
w = Vector(R, Q)
g = Segment(P, Q)
Text5: "m(x_0, x_0+h)=\frac{f(x_0+h)-f(x_0)}{h} = " + (LaTeX[m]) + ""
fmax = Max({f(x0), f(x0 + h)})
c = Circle(P, h / 2)
A, B = Intersect(t, c)
ts = Segment(A, B)
d = true
C: (x(B) | y(P))
i = Vector(C, B)
e = Vector(P, C)
D, E = Intersect(f, c)
f2(x) = If[x(D) ≤ x ≤ x(E), f(x)]
fmin = Min({f(x0), f(x0 + h)})
f1: f'(x0)