x

f(x)=

dx

x_0 =

mittlere Änderungsrate:
Steigung der Sekante:

lokale Änderungsrate:
Steigung im Punkt:

x_0

x_0+h

h \rightarrow 0

\downarrow

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

 f'(x_0) = \lim\limits_{h \rightarrow 0}{\frac{f(x_0+h)-f(x_0)}{h}}

\downarrow

x0 = 1 (slider from -5 to 5, step 0.1)
h = 1 (slider from -1 to 1, step 0.01)
c = 0.25 (slider from -5 to 5, step 0.01)
a = 1 (slider from -5 to 5, step 0.01)
f(x) = If[x < -1, ((-a) * (x + 1)) + c, If[x > 1, (a * (x - 1)) + c, (0.25 * x^(2))]]
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)
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)
k = Circle(P, 0.2)
R = Point(k)
u = Vector(P, R)
w = Vector(R, Q)
g = Segment(P, Q)
f1: f'(x0)
t = Line(P, R)
A, B = Intersect(k, t)
i = Segment(A, B)
Text4: "f'(x_0) =" + f1 + ""
k_{1} = 1 (slider from -5 to 5, step 0.1)
X0: (x0, 0)
X1: (x0 + h1, 0)
x1: x0 + h
Text16: "m(" + x0 + "," + x1 + ") = " + m + ""
Text3: "m(" + x0 + ", " + x1 + ") = " + m + ""
Text17: "f'(" + x0 + ") = " + f1 + ""
Text12: "f'(" + x0 + ") = " + f1 + ""
d: h1 ≟ 0 ∧ x0 ≠ 1