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Funktion: f(x) = x2 - 4, Df = R, Wf = [-4; +∞), entlang der y-Achse nach unten verschobene 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 | 96 | -20 | 2 | 0 | |
-9.5 | 86.25 | -19 | 2 | 0 | |
-9 | 77 | -18 | 2 | 0 | |
-8.5 | 68.25 | -17 | 2 | 0 | |
-8 | 60 | -16 | 2 | 0 | |
-7.5 | 52.25 | -15 | 2 | 0 | |
-7 | 45 | -14 | 2 | 0 | |
-6.5 | 38.25 | -13 | 2 | 0 | |
-6 | 32 | -12 | 2 | 0 | |
-5.5 | 26.25 | -11 | 2 | 0 | |
-5 | 21 | -10 | 2 | 0 | |
-4.5 | 16.25 | -9 | 2 | 0 | |
-4 | 12 | -8 | 2 | 0 | |
-3.5 | 8.25 | -7 | 2 | 0 | |
-3 | 5 | -6 | 2 | 0 | |
-2.5 | 2.25 | -5 | 2 | 0 | |
-2 | 0 | -4 | 2 | 0 | Nullstelle N(-2|0) |
-1.5 | -1.75 | -3 | 2 | 0 | |
-1 | -3 | -2 | 2 | 0 | |
-0.5 | -3.75 | -1 | 2 | 0 | |
0 | -4 | 0 | 2 | 0 | Schnittpunkt Sy(0|-4) = Tiefpunkt T(0|-4) |
0.5 | -3.75 | 1 | 2 | 0 | |
1 | -3 | 2 | 2 | 0 | |
1.5 | -1.75 | 3 | 2 | 0 | |
2 | 0 | 4 | 2 | 0 | Nullstelle N(2|0) |
2.5 | 2.25 | 5 | 2 | 0 | |
3 | 5 | 6 | 2 | 0 | |
3.5 | 8.25 | 7 | 2 | 0 | |
4 | 12 | 8 | 2 | 0 | |
4.5 | 16.25 | 9 | 2 | 0 | |
5 | 21 | 10 | 2 | 0 | |
5.5 | 26.25 | 11 | 2 | 0 | |
6 | 32 | 12 | 2 | 0 | |
6.5 | 38.25 | 13 | 2 | 0 | |
7 | 45 | 14 | 2 | 0 | |
7.5 | 52.25 | 15 | 2 | 0 | |
8 | 60 | 16 | 2 | 0 | |
8.5 | 68.25 | 17 | 2 | 0 | |
9 | 77 | 18 | 2 | 0 | |
9.5 | 86.25 | 19 | 2 | 0 | |
10 | 96 | 20 | 2 | 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