stetig?

diffbar?

Stetigkeit und Differenzierbarkeit
(Veranschaulichung)

... an der Stelle x_0

Variation

f0(x) = 1 / 15 * x^(3) - 3 / 5 * x^(2) + 21 / 5
x_0 = 2 (slider from -1 to 7, step 0.2)
f = Function(f0, -20, x_0)
a = 0.3 (slider from -2 to 2, step 0.02)
ga: 1 / 15 + a / 10
g0(x) = ga * x^(3) + (x_0 / 10 - 3 / 5 - 3 / 2 * ga * x_0) * x^(2) - 1 / 30 * x_0^(3) + 21 / 5 + 1 / 2 * ga * x_0^(3)
g = Function(g0, x_0, 40)
P: (x_0, f(x_0))
v: 2 * a
h0(x) = 1 / 15 * x^(3) - (6 - 5 * v / x_0) / 10 * x^(2) + (42 - 5 * x_0 * v) / 10
h = Function(h0, x_0, 40)
k0(x) = f0(x) + a
k = Function(k0, x_0, 40)
P_0: (x_0, 0)
P_k: (x_0, k(x_0))
s1 = Segment(P_0, P)
s2 = Segment(P_0, P_k)
ste = true
db = true
f1 = Derivative(f)
h1 = Derivative(h)
tf(x) = f1(x_0) * (x - x_0) + f(x_0)
th(x) = h1(x_0) * (x - x_0) + h(x_0)