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Funktion: f(x) = x2/5 + 3x/8 - 22/15, Df = R, Wf = [-1.6424; +∞), allgemeine Parabel (Normalform), Funktion achsensymmetrisch zur Senkrechten x = -0.938, x -> -∞: f(x) -> +∞, x -> +∞: f(x) -> +∞ ->
Wertetabelle: | |||||
x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
-10 | 14.7833 | -3.63 | 0.4 | 0 | |
-9.5 | 13.0208 | -3.42 | 0.4 | 0 | |
-9 | 11.3583 | -3.23 | 0.4 | 0 | |
-8.5 | 9.7958 | -3.03 | 0.4 | 0 | |
-8 | 8.3333 | -2.83 | 0.4 | 0 | |
-7.5 | 6.9708 | -2.62 | 0.4 | 0 | |
-7 | 5.7083 | -2.42 | 0.4 | 0 | |
-6.5 | 4.5458 | -2.23 | 0.4 | 0 | |
-6 | 3.4833 | -2.02 | 0.4 | 0 | |
-5.5 | 2.5208 | -1.82 | 0.4 | 0 | |
-5 | 1.6583 | -1.62 | 0.4 | 0 | |
-4.5 | 0.8958 | -1.42 | 0.4 | 0 | |
-4 | 0.2333 | -1.22 | 0.4 | 0 | |
-3.804 | 0 | -1.15 | 0.4 | 0 | Nullstelle N(-3.8|0) |
-3.5 | -0.3292 | -1.03 | 0.4 | 0 | |
-3 | -0.7917 | -0.82 | 0.4 | 0 | |
-2.5 | -1.1542 | -0.63 | 0.4 | 0 | |
-2 | -1.4167 | -0.42 | 0.4 | 0 | |
-1.5 | -1.5792 | -0.22 | 0.4 | 0 | |
-1 | -1.6417 | -0.02 | 0.4 | 0 | |
-0.938 | -1.6424 | 0 | 0.4 | 0 | Tiefpunkt T(-0.94|-1.64) |
-0.5 | -1.6042 | 0.17 | 0.4 | 0 | |
0 | -1.4667 | 0.38 | 0.4 | 0 | Schnittpunkt Sy(0|-1.47) |
0.5 | -1.2292 | 0.57 | 0.4 | 0 | |
1 | -0.8917 | 0.77 | 0.4 | 0 | |
1.5 | -0.4542 | 0.98 | 0.4 | 0 | |
1.928 | 0 | 1.15 | 0.4 | 0 | Nullstelle N(1.93|0) |
2 | 0.0833 | 1.17 | 0.4 | 0 | |
2.5 | 0.7208 | 1.38 | 0.4 | 0 | |
3 | 1.4583 | 1.57 | 0.4 | 0 | |
3.5 | 2.2958 | 1.78 | 0.4 | 0 | |
4 | 3.2333 | 1.98 | 0.4 | 0 | |
4.5 | 4.2708 | 2.18 | 0.4 | 0 | |
5 | 5.4083 | 2.38 | 0.4 | 0 | |
5.5 | 6.6458 | 2.58 | 0.4 | 0 | |
6 | 7.9833 | 2.78 | 0.4 | 0 | |
6.5 | 9.4208 | 2.98 | 0.4 | 0 | |
7 | 10.9583 | 3.17 | 0.4 | 0 | |
7.5 | 12.5958 | 3.38 | 0.4 | 0 | |
8 | 14.3333 | 3.58 | 0.4 | 0 | |
8.5 | 16.1708 | 3.77 | 0.4 | 0 | |
9 | 18.1083 | 3.98 | 0.4 | 0 | |
9.5 | 20.1458 | 4.17 | 0.4 | 0 | |
10 | 22.2833 | 4.37 | 0.4 | 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