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Funktion: f(x) = (x+5)2, Df = R, Wf = [0; +∞), entlang der x-Achse nach links verschobene Normalparabel (Scheitelform), Funktion achsensymmetrisch zur Senkrechten x = -5, x -> -∞: f(x) -> +∞, x -> +∞: f(x) -> +∞ ->
Wertetabelle: | |||||
x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
-10 | 25 | -10 | 2 | 0 | |
-9.5 | 20.25 | -9 | 2 | 0 | |
-9 | 16 | -8 | 2 | 0 | |
-8.5 | 12.25 | -7 | 2 | 0 | |
-8 | 9 | -6 | 2 | 0 | |
-7.5 | 6.25 | -5 | 2 | 0 | |
-7 | 4 | -4 | 2 | 0 | |
-6.5 | 2.25 | -3 | 2 | 0 | |
-6 | 1 | -2 | 2 | 0 | |
-5.5 | 0.25 | -1 | 2 | 0 | |
-5 | 0 | 0 | 2 | 0 | Nullstelle N(-5|0) = Tiefpunkt T(-5|0) |
-4.5 | 0.25 | 1 | 2 | 0 | |
-4 | 1 | 2 | 2 | 0 | |
-3.5 | 2.25 | 3 | 2 | 0 | |
-3 | 4 | 4 | 2 | 0 | |
-2.5 | 6.25 | 5 | 2 | 0 | |
-2 | 9 | 6 | 2 | 0 | |
-1.5 | 12.25 | 7 | 2 | 0 | |
-1 | 16 | 8 | 2 | 0 | |
-0.5 | 20.25 | 9 | 2 | 0 | |
0 | 25 | 10 | 2 | 0 | Schnittpunkt Sy(0|25) |
0.5 | 30.25 | 11 | 2 | 0 | |
1 | 36 | 12 | 2 | 0 | |
1.5 | 42.25 | 13 | 2 | 0 | |
2 | 49 | 14 | 2 | 0 | |
2.5 | 56.25 | 15 | 2 | 0 | |
3 | 64 | 16 | 2 | 0 | |
3.5 | 72.25 | 17 | 2 | 0 | |
4 | 81 | 18 | 2 | 0 | |
4.5 | 90.25 | 19 | 2 | 0 | |
5 | 100 | 20 | 2 | 0 | |
5.5 | 110.25 | 21 | 2 | 0 | |
6 | 121 | 22 | 2 | 0 | |
6.5 | 132.25 | 23 | 2 | 0 | |
7 | 144 | 24 | 2 | 0 | |
7.5 | 156.25 | 25 | 2 | 0 | |
8 | 169 | 26 | 2 | 0 | |
8.5 | 182.25 | 27 | 2 | 0 | |
9 | 196 | 28 | 2 | 0 | |
9.5 | 210.25 | 29 | 2 | 0 | |
10 | 225 | 30 | 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