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Funktion: f(x) = 0.25·(x-1)3 + 2, Df = R, Wf = R, Potenzfunktion 3. Grades, entlang der x-Achse und y-Achse verschoben, Funktion punktsymmetrisch zum Punkt W(1|2), x -> -∞: f(x) -> -∞, x -> +∞: f(x) -> +∞ ->
Wertetabelle: | |||||
x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
-10 | -330.75 | 90.75 | -16.5 | 1.5 | |
-9.5 | -287.4062 | 82.69 | -15.75 | 1.5 | |
-9 | -248 | 75 | -15 | 1.5 | |
-8.5 | -212.3437 | 67.69 | -14.25 | 1.5 | |
-8 | -180.25 | 60.75 | -13.5 | 1.5 | |
-7.5 | -151.5312 | 54.19 | -12.75 | 1.5 | |
-7 | -126 | 48 | -12 | 1.5 | |
-6.5 | -103.4687 | 42.19 | -11.25 | 1.5 | |
-6 | -83.75 | 36.75 | -10.5 | 1.5 | |
-5.5 | -66.6562 | 31.69 | -9.75 | 1.5 | |
-5 | -52 | 27 | -9 | 1.5 | |
-4.5 | -39.5937 | 22.69 | -8.25 | 1.5 | |
-4 | -29.25 | 18.75 | -7.5 | 1.5 | |
-3.5 | -20.7812 | 15.19 | -6.75 | 1.5 | |
-3 | -14 | 12 | -6 | 1.5 | |
-2.5 | -8.7187 | 9.19 | -5.25 | 1.5 | |
-2 | -4.75 | 6.75 | -4.5 | 1.5 | |
-1.5 | -1.9062 | 4.69 | -3.75 | 1.5 | |
-1 | 0 | 3 | -3 | 1.5 | Nullstelle N(-1|0) |
-0.5 | 1.1563 | 1.69 | -2.25 | 1.5 | |
0 | 1.75 | 0.75 | -1.5 | 1.5 | Schnittpunkt Sy(0|1.75) |
0.5 | 1.9688 | 0.19 | -0.75 | 1.5 | |
1 | 2 | 0 | 0 | 1.5 | Wendepunkt W(1|2) = Sattelpunkt WS(1|2) |
1.5 | 2.0313 | 0.19 | 0.75 | 1.5 | |
2 | 2.25 | 0.75 | 1.5 | 1.5 | |
2.5 | 2.8438 | 1.69 | 2.25 | 1.5 | |
3 | 4 | 3 | 3 | 1.5 | |
3.5 | 5.9063 | 4.69 | 3.75 | 1.5 | |
4 | 8.75 | 6.75 | 4.5 | 1.5 | |
4.5 | 12.7188 | 9.19 | 5.25 | 1.5 | |
5 | 18 | 12 | 6 | 1.5 | |
5.5 | 24.7813 | 15.19 | 6.75 | 1.5 | |
6 | 33.25 | 18.75 | 7.5 | 1.5 | |
6.5 | 43.5938 | 22.69 | 8.25 | 1.5 | |
7 | 56 | 27 | 9 | 1.5 | |
7.5 | 70.6563 | 31.69 | 9.75 | 1.5 | |
8 | 87.75 | 36.75 | 10.5 | 1.5 | |
8.5 | 107.4688 | 42.19 | 11.25 | 1.5 | |
9 | 130 | 48 | 12 | 1.5 | |
9.5 | 155.5313 | 54.19 | 12.75 | 1.5 | |
10 | 184.25 | 60.75 | 13.5 | 1.5 | |
Graph: | |||||
Abkürzungen: Df = (maximaler) Definitionsbereich, f(x) = Funktion, f'(x) = 1. Ableitung, f''(x) = 2. Ableitung, f'''(x) = 3. Ableitung, H = Hochpunkt, N = Nullstelle, P = Polstelle, R = reelle Zahlen, T = Tiefpunkt, W = Wendepunkt, WS = Sattelpunkt, Wf = Wertebereich, {.} = ein-/mehrelementige Menge, [.; .] = abgeschlossenes Intervall, (.; .) = offenes Intervall, [.; .), (.; .] = halboffenes Intervall, ∞ = unendlich.
Bearbeiter: Michael Buhlmann