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Funktion: f(x) = 0.5x2, Df = R, Wf = [0; +∞), allgemeine Parabel als gestauchte Normalparabel, Funktion achsensymmetrisch zur Senkrechten x = 0, x -> -∞: f(x) -> +∞, x -> +∞: f(x) -> +∞ ->
Wertetabelle: | |||||
x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
-10 | 50 | -10 | 1 | 0 | |
-9.5 | 45.125 | -9.5 | 1 | 0 | |
-9 | 40.5 | -9 | 1 | 0 | |
-8.5 | 36.125 | -8.5 | 1 | 0 | |
-8 | 32 | -8 | 1 | 0 | |
-7.5 | 28.125 | -7.5 | 1 | 0 | |
-7 | 24.5 | -7 | 1 | 0 | |
-6.5 | 21.125 | -6.5 | 1 | 0 | |
-6 | 18 | -6 | 1 | 0 | |
-5.5 | 15.125 | -5.5 | 1 | 0 | |
-5 | 12.5 | -5 | 1 | 0 | |
-4.5 | 10.125 | -4.5 | 1 | 0 | |
-4 | 8 | -4 | 1 | 0 | |
-3.5 | 6.125 | -3.5 | 1 | 0 | |
-3 | 4.5 | -3 | 1 | 0 | |
-2.5 | 3.125 | -2.5 | 1 | 0 | |
-2 | 2 | -2 | 1 | 0 | |
-1.5 | 1.125 | -1.5 | 1 | 0 | |
-1 | 0.5 | -1 | 1 | 0 | |
-0.5 | 0.125 | -0.5 | 1 | 0 | |
0 | 0 | 0 | 1 | 0 | Nullstelle N(0|0) = Schnittpunkt Sy(0|0) = Tiefpunkt T(0|0) |
0.5 | 0.125 | 0.5 | 1 | 0 | |
1 | 0.5 | 1 | 1 | 0 | |
1.5 | 1.125 | 1.5 | 1 | 0 | |
2 | 2 | 2 | 1 | 0 | |
2.5 | 3.125 | 2.5 | 1 | 0 | |
3 | 4.5 | 3 | 1 | 0 | |
3.5 | 6.125 | 3.5 | 1 | 0 | |
4 | 8 | 4 | 1 | 0 | |
4.5 | 10.125 | 4.5 | 1 | 0 | |
5 | 12.5 | 5 | 1 | 0 | |
5.5 | 15.125 | 5.5 | 1 | 0 | |
6 | 18 | 6 | 1 | 0 | |
6.5 | 21.125 | 6.5 | 1 | 0 | |
7 | 24.5 | 7 | 1 | 0 | |
7.5 | 28.125 | 7.5 | 1 | 0 | |
8 | 32 | 8 | 1 | 0 | |
8.5 | 36.125 | 8.5 | 1 | 0 | |
9 | 40.5 | 9 | 1 | 0 | |
9.5 | 45.125 | 9.5 | 1 | 0 | |
10 | 50 | 10 | 1 | 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