Tangente in x_0

Sekante PQ

Steigungsdreieck Sekante

Steigungsdreieck Tangente

x_0+h

f(x_0+h)-f(x_0)

x_0 = 1.6000000000000005 (slider from -4 to 9, step 0.1)
h = 2.1000000000000005 (slider from -2 to 10, step 0.1)
f(x) = 0.03 * x^(3.0)
c: f(x_0 + h) - f(x_0)
X_{x_0}: (x_0, 0.0)
P_{x_0}: (x_0, f(x_0))
X_{x_0+h}: (x_0 + h, 0.0)
Q_{x_0+h}: (x_0 + h, f(x_0 + h))
HP: (x_0 + h, f(x_0))
a = Segment(P_{x_0}, HP)
b = Segment(HP, Q_{x_0+h})
m: (f(x_0 + h) - f(x_0)) / h
s(x) = m * (x - x_0) + f(x_0)
t(x) = f'(x_0) * (x - x_0) + f(x_0)
h_f: "h=" + h
A = Midpoint(a)
B = Midpoint(b)
d = false
e = false
g = true
i = false
HP_2: (x_0 + 1.0, t(x_0))
HP_3: (x_0 + 1.0, t(x_0 + 1.0))
j = Segment(HP_3, HP_2)
k = Segment(HP_2, P_{x_0})
X_0: "x_0=" + x_0