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Funktion: f(x) = x2 + 11x/3, Df = R, Wf = [-3.3611; +∞), verschobene Normalparabel (Normalform), Funktion achsensymmetrisch zur Senkrechten x = -1.8333, x -> -∞: f(x) -> +∞, x -> +∞: f(x) -> +∞ ->
Wertetabelle: | |||||
x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
-10 | 63.3333 | -16.33 | 2 | 0 | |
-9.5 | 55.4167 | -15.33 | 2 | 0 | |
-9 | 48 | -14.33 | 2 | 0 | |
-8.5 | 41.0833 | -13.33 | 2 | 0 | |
-8 | 34.6667 | -12.33 | 2 | 0 | |
-7.5 | 28.75 | -11.33 | 2 | 0 | |
-7 | 23.3333 | -10.33 | 2 | 0 | |
-6.5 | 18.4167 | -9.33 | 2 | 0 | |
-6 | 14 | -8.33 | 2 | 0 | |
-5.5 | 10.0833 | -7.33 | 2 | 0 | |
-5 | 6.6667 | -6.33 | 2 | 0 | |
-4.5 | 3.75 | -5.33 | 2 | 0 | |
-4 | 1.3333 | -4.33 | 2 | 0 | |
-3.667 | 0 | -3.67 | 2 | 0 | Nullstelle N(-3.67|0) |
-3.5 | -0.5833 | -3.33 | 2 | 0 | |
-3 | -2 | -2.33 | 2 | 0 | |
-2.5 | -2.9167 | -1.33 | 2 | 0 | |
-2 | -3.3333 | -0.33 | 2 | 0 | |
-1.834 | -3.3611 | 0 | 2 | 0 | Tiefpunkt T(-1.83|-3.36) |
-1.5 | -3.25 | 0.67 | 2 | 0 | |
-1 | -2.6667 | 1.67 | 2 | 0 | |
-0.5 | -1.5833 | 2.67 | 2 | 0 | |
0 | 0 | 3.67 | 2 | 0 | Nullstelle N(0|0) = Schnittpunkt Sy(0|0) |
0.5 | 2.0833 | 4.67 | 2 | 0 | |
1 | 4.6667 | 5.67 | 2 | 0 | |
1.5 | 7.75 | 6.67 | 2 | 0 | |
2 | 11.3333 | 7.67 | 2 | 0 | |
2.5 | 15.4167 | 8.67 | 2 | 0 | |
3 | 20 | 9.67 | 2 | 0 | |
3.5 | 25.0833 | 10.67 | 2 | 0 | |
4 | 30.6667 | 11.67 | 2 | 0 | |
4.5 | 36.75 | 12.67 | 2 | 0 | |
5 | 43.3333 | 13.67 | 2 | 0 | |
5.5 | 50.4167 | 14.67 | 2 | 0 | |
6 | 58 | 15.67 | 2 | 0 | |
6.5 | 66.0833 | 16.67 | 2 | 0 | |
7 | 74.6667 | 17.67 | 2 | 0 | |
7.5 | 83.75 | 18.67 | 2 | 0 | |
8 | 93.3333 | 19.67 | 2 | 0 | |
8.5 | 103.4167 | 20.67 | 2 | 0 | |
9 | 114 | 21.67 | 2 | 0 | |
9.5 | 125.0833 | 22.67 | 2 | 0 | |
10 | 136.6667 | 23.67 | 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