$f$

x

f(x)=

dx

$x = $

mittlere Änderungsrate:
Steigung der Sekante:

lokale Änderungsrate:
Steigung im Punkt:

$t$

x

x+h

h \rightarrow 0

\downarrow

m(x, x+h)=\frac{f(x+h)-f(x)}{h}

 f'(x) = \lim\limits_{h \rightarrow 0}{\frac{f(x+h)-f(x)}{h}}

\downarrow

$f'$

f(x) = x^2

= 2x + h

= 2x

$f(x) = $

$f'$

$f'(x) = $

h =

Kontrolle

Spur

Tangente

f(x) = x^(2)
xPunkte = Sequence((i, 0), i, -4.5, 4.5, 0.5)
X0 = Point(xPunkte)
x0: x(X0)
h: 0
Q: (x0 + h, f(x0 + h))
P: (x0, f(x0))
h1: x(Q) - x(P)
df: f(x0 + h1) - f(x0)
dx = 1 (slider from -5 to 5, step 0.1)
xmin = -2 (slider from -5 to 5, step 0.1)
xmax = 2 (slider from -5 to 10, step 0.1)
a = 1
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))])
b = 1 (slider from xmin to xmax, step dx)
ma = 1 (slider from -5 to 5, step 0.1)
Eingabefeld1 = Textfield(f)
Eingabefeld4 = Textfield(dx)
s = Line(P, Q)
m: df / h1
Eingabefeld5 = Textfield(x0)
R: (x(Q), y(P))
u = Vector(P, R)
w = Vector(R, Q)
g = Segment(P, Q)
f1x0: f'(x0)
t(x) = (f1x0 * (x - x0)) + f(x0)
c = Circle(P, 0.2)
A, B = Intersect(t, c)
i = Segment(A, B)
Text4: "f'(x_0) =" + f1x0 + ""
k = 1 (slider from -5 to 5, step 0.1)
X1: (x0 + h1, 0)
x1: x0 + h
Text3: "m(" + x0 + ", " + x1 + ") = " + m + ""
f1(x) = f'(x)
Eingabefeld2 = Textfield(f)
gL: -4.5
gR: 4.5
gU1: -1
gO1: 3
gU2: -2
gO2: 2
gl1: x = 3
fEingabe(x) = (2 * x)
Eingabefeld3 = Textfield(fEingabe)
Text15: "f'(" + (LaTeX[x0]) + ") = " + (LaTeX[f1x0]) + ""
Text12: "f'(" + (LaTeX[x0]) + ") = " + (LaTeX[f1x0]) + ""
Eingabefeld6 = Textfield(h)
d = false
Z0: (x0, f1(x0))
e = true
f1Punke = Sequence((i, f1(i)), i, -4.5, 4.5, 0.5)
j = false