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Funktion: f(x) = 0.2·(x+3)(x-1)(x-5), Df = R, Wf = R, Polynom 3. Grades (Produktform), Funktion punktsymmetrisch zum Punkt W(1|0), x -> -∞: f(x) -> -∞, x -> +∞: f(x) -> +∞ ->
Wertetabelle: | |||||
x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
-10 | -231 | 69.4 | -13.2 | 1.2 | |
-9.5 | -197.925 | 62.95 | -12.6 | 1.2 | |
-9 | -168 | 56.8 | -12 | 1.2 | |
-8.5 | -141.075 | 50.95 | -11.4 | 1.2 | |
-8 | -117 | 45.4 | -10.8 | 1.2 | |
-7.5 | -95.625 | 40.15 | -10.2 | 1.2 | |
-7 | -76.8 | 35.2 | -9.6 | 1.2 | |
-6.5 | -60.375 | 30.55 | -9 | 1.2 | |
-6 | -46.2 | 26.2 | -8.4 | 1.2 | |
-5.5 | -34.125 | 22.15 | -7.8 | 1.2 | |
-5 | -24 | 18.4 | -7.2 | 1.2 | |
-4.5 | -15.675 | 14.95 | -6.6 | 1.2 | |
-4 | -9 | 11.8 | -6 | 1.2 | |
-3.5 | -3.825 | 8.95 | -5.4 | 1.2 | |
-3 | 0 | 6.4 | -4.8 | 1.2 | Nullstelle N(-3|0) |
-2.5 | 2.625 | 4.15 | -4.2 | 1.2 | |
-2 | 4.2 | 2.2 | -3.6 | 1.2 | |
-1.5 | 4.875 | 0.55 | -3 | 1.2 | |
-1.31 | 4.9267 | 0 | -2.77 | 1.2 | Hochpunkt H(-1.31|4.93) |
-1 | 4.8 | -0.8 | -2.4 | 1.2 | |
-0.5 | 4.125 | -1.85 | -1.8 | 1.2 | |
0 | 3 | -2.6 | -1.2 | 1.2 | Schnittpunkt Sy(0|3) |
0.5 | 1.575 | -3.05 | -0.6 | 1.2 | |
1 | 0 | -3.2 | 0 | 1.2 | Nullstelle N(1|0) = Wendepunkt W(1|0) |
1.5 | -1.575 | -3.05 | 0.6 | 1.2 | |
2 | -3 | -2.6 | 1.2 | 1.2 | |
2.5 | -4.125 | -1.85 | 1.8 | 1.2 | |
3 | -4.8 | -0.8 | 2.4 | 1.2 | |
3.308 | -4.9267 | 0 | 2.77 | 1.2 | Tiefpunkt T(3.31|-4.93) |
3.5 | -4.875 | 0.55 | 3 | 1.2 | |
4 | -4.2 | 2.2 | 3.6 | 1.2 | |
4.5 | -2.625 | 4.15 | 4.2 | 1.2 | |
5 | 0 | 6.4 | 4.8 | 1.2 | Nullstelle N(5|0) |
5.5 | 3.825 | 8.95 | 5.4 | 1.2 | |
6 | 9 | 11.8 | 6 | 1.2 | |
6.5 | 15.675 | 14.95 | 6.6 | 1.2 | |
7 | 24 | 18.4 | 7.2 | 1.2 | |
7.5 | 34.125 | 22.15 | 7.8 | 1.2 | |
8 | 46.2 | 26.2 | 8.4 | 1.2 | |
8.5 | 60.375 | 30.55 | 9 | 1.2 | |
9 | 76.8 | 35.2 | 9.6 | 1.2 | |
9.5 | 95.625 | 40.15 | 10.2 | 1.2 | |
10 | 117 | 45.4 | 10.8 | 1.2 | |
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