x

f(x)=

dx

x_0 =

mittlere Änderungsrate:
Steigung der Sekante:

lokale Änderungsrate:
Steigung im Punkt:

x_0

x_0+h

h \rightarrow 0

f'(x_0) 

m(x_0, x_0+h)

h =

f'(x_0) verdeutlichen

Koordinaten anzeigen

mittlere Änderungsrate anzeigen

f(x) = x^(4) - (2 * x^(2))
x0: 0
h: 0.5
Q: (x0 + h, f(x0 + h))
P: (x0, f(x0))
df: f(x0 + h) - 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 / h
Eingabefeld5 = Textfield(x0)
R: (x(Q), y(P))
u = Vector(P, R)
w = Vector(R, Q)
Text5: "m(x_0, x_0+h)=\frac{f(x_0+h)-f(x_0)}{h} = " + (LaTeX[m]) + ""
f1: f'(x0)
t(x) = (f1 * (x - x0)) + f(x0)
c = Circle(P, 0.2)
A, B = Intersect(t, c)
i = Segment(A, B)
Text3: "m(x_0, x_0 + h) = " + m + ""
k = 1 (slider from -5 to 5, step 0.1)
X0: (x0, 0)
X1: (x0 + h, 0)
v = Vector((1, 4), (1, 3.1))
Text6: " f'(x_0) = \lim\limits_{h \rightarrow 0}{\frac{f(x_0+h-f(x_0)}{h}}= " + (LaTeX[f1]) + ""
d = true
Eingabefeld2 = Textfield(h)
e = false
g = Line(P, Q)
j = false
Text11: "P" + P + "
Q" + Q + ""
l = false
Text12: "m(x_0,x_0+h) = " + m + ""