f

P'

f'

Ausgangsfunktion

Ableitungsfunktion

Tangente

f = 1 (slider from -5 to 5)
h1(x) = (-197 / 5625 * x^(6)) + (43751 / 67500 * x^(5)) - (105487 / 22500 * x^(4)) + (7923 / 500 * x^(3)) - (57547 / 2700 * x^(2)) + 20
h2(x) = (4295 / 4148928 * x^(6)) - (11467 / 345744 * x^(5)) + (163375 / 691488 * x^(4)) + (2932205 / 1037232 * x^(3)) - (23552785 / 460992 * x^(2)) + (5090025 / 19208 * x) - 4276211 / 9604
f0(x) = If[-0.1 ≤ x ≤ 5, (0.25 * h1(x)), If[5 ≤ x ≤ 12.1, (0.25 * h2(x))]]
PGraph = Sequence((i, f0(i)), i, 0, 12)
P = Point(f0)
P1: (x(P), f0'(x(P)))
APunkte = Sequence((i, f0'(i)), i, 0, 12)
PListe: {}
f1(x) = f0'(x)
b: h2''(5)
c: h1''(5)
t = Tangent(P, f0)
k = Circle(P, 0.5)
A, B = Intersect(k, t)
g = Segment(A, B)
xP: x(P)
m: f1(xP)
Text3: "f'(" + xP + ")=" + m + ""
gl1: x = xP
a = false
P': (x(P), f1(x(P)))