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Funktion: f(x) = x3-4x, Df = R, Wf = R, Polynom 3. Grades, Funktion punktsymmetrisch zum Punkt O(0|0), x -> -∞: f(x) -> -∞, x -> +∞: f(x) -> +∞ ->
Wertetabelle: | |||||
x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
-10 | -960 | 296 | -60 | 6 | |
-9.5 | -819.375 | 266.75 | -57 | 6 | |
-9 | -693 | 239 | -54 | 6 | |
-8.5 | -580.125 | 212.75 | -51 | 6 | |
-8 | -480 | 188 | -48 | 6 | |
-7.5 | -391.875 | 164.75 | -45 | 6 | |
-7 | -315 | 143 | -42 | 6 | |
-6.5 | -248.625 | 122.75 | -39 | 6 | |
-6 | -192 | 104 | -36 | 6 | |
-5.5 | -144.375 | 86.75 | -33 | 6 | |
-5 | -105 | 71 | -30 | 6 | |
-4.5 | -73.125 | 56.75 | -27 | 6 | |
-4 | -48 | 44 | -24 | 6 | |
-3.5 | -28.875 | 32.75 | -21 | 6 | |
-3 | -15 | 23 | -18 | 6 | |
-2.5 | -5.625 | 14.75 | -15 | 6 | |
-2 | 0 | 8 | -12 | 6 | Nullstelle N(-2|0) |
-1.5 | 2.625 | 2.75 | -9 | 6 | |
-1.156 | 3.0792 | 0.01 | -6.94 | 6 | Hochpunkt H(-1.16|3.08) |
-1 | 3 | -1 | -6 | 6 | |
-0.5 | 1.875 | -3.25 | -3 | 6 | |
0 | 0 | -4 | 0 | 6 | Nullstelle N(0|0) = Schnittpunkt Sy(0|0) = Wendepunkt W(0|0) |
0.5 | -1.875 | -3.25 | 3 | 6 | |
1 | -3 | -1 | 6 | 6 | |
1.154 | -3.0792 | 0 | 6.92 | 6 | Tiefpunkt T(1.15|-3.08) |
1.5 | -2.625 | 2.75 | 9 | 6 | |
2 | 0 | 8 | 12 | 6 | Nullstelle N(2|0) |
2.5 | 5.625 | 14.75 | 15 | 6 | |
3 | 15 | 23 | 18 | 6 | |
3.5 | 28.875 | 32.75 | 21 | 6 | |
4 | 48 | 44 | 24 | 6 | |
4.5 | 73.125 | 56.75 | 27 | 6 | |
5 | 105 | 71 | 30 | 6 | |
5.5 | 144.375 | 86.75 | 33 | 6 | |
6 | 192 | 104 | 36 | 6 | |
6.5 | 248.625 | 122.75 | 39 | 6 | |
7 | 315 | 143 | 42 | 6 | |
7.5 | 391.875 | 164.75 | 45 | 6 | |
8 | 480 | 188 | 48 | 6 | |
8.5 | 580.125 | 212.75 | 51 | 6 | |
9 | 693 | 239 | 54 | 6 | |
9.5 | 819.375 | 266.75 | 57 | 6 | |
10 | 960 | 296 | 60 | 6 | |
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