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Funktion: f(x) = 0.5·(2x+3)(3x-4), Df = R, Wf = [-6.021; +∞), allgemeine Parabel (2. Grades; Produktform), Funktion achsensymmetrisch zur Senkrechten x = -1/12, x -> -∞: f(x) -> +∞, x -> +∞: f(x) -> +∞ ->
Wertetabelle: | |||||
x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
-10 | 289 | -59.5 | 6 | 0 | |
-9.5 | 260 | -56.5 | 6 | 0 | |
-9 | 232.5 | -53.5 | 6 | 0 | |
-8.5 | 206.5 | -50.5 | 6 | 0 | |
-8 | 182 | -47.5 | 6 | 0 | |
-7.5 | 159 | -44.5 | 6 | 0 | |
-7 | 137.5 | -41.5 | 6 | 0 | |
-6.5 | 117.5 | -38.5 | 6 | 0 | |
-6 | 99 | -35.5 | 6 | 0 | |
-5.5 | 82 | -32.5 | 6 | 0 | |
-5 | 66.5 | -29.5 | 6 | 0 | |
-4.5 | 52.5 | -26.5 | 6 | 0 | |
-4 | 40 | -23.5 | 6 | 0 | |
-3.5 | 29 | -20.5 | 6 | 0 | |
-3 | 19.5 | -17.5 | 6 | 0 | |
-2.5 | 11.5 | -14.5 | 6 | 0 | |
-2 | 5 | -11.5 | 6 | 0 | |
-1.5 | 0 | -8.5 | 6 | 0 | Nullstelle N(-1.5|0) |
-1 | -3.5 | -5.5 | 6 | 0 | |
-0.5 | -5.5 | -2.5 | 6 | 0 | |
-0.083 | -6.02083 | -0.04 | 6 | 0 | Tiefpunkt T(-0.083|-6.021) |
0 | -6 | 0.5 | 6 | 0 | Schnittpunkt Sy(0|-6) |
0.5 | -5 | 3.5 | 6 | 0 | |
1 | -2.5 | 6.5 | 6 | 0 | |
1.33 | 0 | 8.48 | 6 | 0 | Nullstelle N(1.33|0) |
1.5 | 1.5 | 9.5 | 6 | 0 | |
2 | 7 | 12.5 | 6 | 0 | |
2.5 | 14 | 15.5 | 6 | 0 | |
3 | 22.5 | 18.5 | 6 | 0 | |
3.5 | 32.5 | 21.5 | 6 | 0 | |
4 | 44 | 24.5 | 6 | 0 | |
4.5 | 57 | 27.5 | 6 | 0 | |
5 | 71.5 | 30.5 | 6 | 0 | |
5.5 | 87.5 | 33.5 | 6 | 0 | |
6 | 105 | 36.5 | 6 | 0 | |
6.5 | 124 | 39.5 | 6 | 0 | |
7 | 144.5 | 42.5 | 6 | 0 | |
7.5 | 166.5 | 45.5 | 6 | 0 | |
8 | 190 | 48.5 | 6 | 0 | |
8.5 | 215 | 51.5 | 6 | 0 | |
9 | 241.5 | 54.5 | 6 | 0 | |
9.5 | 269.5 | 57.5 | 6 | 0 | |
10 | 299 | 60.5 | 6 | 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