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Funktion: f(x) = (x2+2x+3)/6, Df = R, Wf = [1/3; +∞), allgemeine Parabel (2. Grades), Funktion achsensymmetrisch zur Senkrechten x = -1, x -> -∞: f(x) -> +∞, x -> +∞: f(x) -> +∞ ->
Wertetabelle: | |||||
x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
-10 | 13.8333 | -3 | 0.33 | 0 | |
-9.5 | 12.375 | -2.83 | 0.33 | 0 | |
-9 | 11 | -2.67 | 0.33 | 0 | |
-8.5 | 9.7083 | -2.5 | 0.33 | 0 | |
-8 | 8.5 | -2.33 | 0.33 | 0 | |
-7.5 | 7.375 | -2.17 | 0.33 | 0 | |
-7 | 6.3333 | -2 | 0.33 | 0 | |
-6.5 | 5.375 | -1.83 | 0.33 | 0 | |
-6 | 4.5 | -1.67 | 0.33 | 0 | |
-5.5 | 3.7083 | -1.5 | 0.33 | 0 | |
-5 | 3 | -1.33 | 0.33 | 0 | |
-4.5 | 2.375 | -1.17 | 0.33 | 0 | |
-4 | 1.8333 | -1 | 0.33 | 0 | |
-3.5 | 1.375 | -0.83 | 0.33 | 0 | |
-3 | 1 | -0.67 | 0.33 | 0 | |
-2.5 | 0.7083 | -0.5 | 0.33 | 0 | |
-2 | 0.5 | -0.33 | 0.33 | 0 | |
-1.5 | 0.375 | -0.17 | 0.33 | 0 | |
-1 | 0.3333 | 0 | 0.33 | 0 | Tiefpunkt T(-1|0.33) |
-0.5 | 0.375 | 0.17 | 0.33 | 0 | |
0 | 0.5 | 0.33 | 0.33 | 0 | Schnittpunkt Sy(0|0.5) |
0.5 | 0.7083 | 0.5 | 0.33 | 0 | |
1 | 1 | 0.67 | 0.33 | 0 | |
1.5 | 1.375 | 0.83 | 0.33 | 0 | |
2 | 1.8333 | 1 | 0.33 | 0 | |
2.5 | 2.375 | 1.17 | 0.33 | 0 | |
3 | 3 | 1.33 | 0.33 | 0 | |
3.5 | 3.7083 | 1.5 | 0.33 | 0 | |
4 | 4.5 | 1.67 | 0.33 | 0 | |
4.5 | 5.375 | 1.83 | 0.33 | 0 | |
5 | 6.3333 | 2 | 0.33 | 0 | |
5.5 | 7.375 | 2.17 | 0.33 | 0 | |
6 | 8.5 | 2.33 | 0.33 | 0 | |
6.5 | 9.7083 | 2.5 | 0.33 | 0 | |
7 | 11 | 2.67 | 0.33 | 0 | |
7.5 | 12.375 | 2.83 | 0.33 | 0 | |
8 | 13.8333 | 3 | 0.33 | 0 | |
8.5 | 15.375 | 3.17 | 0.33 | 0 | |
9 | 17 | 3.33 | 0.33 | 0 | |
9.5 | 18.7083 | 3.5 | 0.33 | 0 | |
10 | 20.5 | 3.67 | 0.33 | 0 | |
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