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Funktion: f(x) = x3 + 8x2, Df = R, Wf = R, Polynom 3. Grades, Funktion punktsymmetrisch zum Punkt W(-8/3|1024/27), x -> -∞: f(x) -> -∞, x -> +∞: f(x) -> +∞ ->
Wertetabelle: | |||||
x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
-10 | -200 | 140 | -44 | 6 | |
-9.5 | -135.375 | 118.75 | -41 | 6 | |
-9 | -81 | 99 | -38 | 6 | |
-8.5 | -36.125 | 80.75 | -35 | 6 | |
-8 | 0 | 64 | -32 | 6 | Nullstelle N(-8|0) |
-7.5 | 28.125 | 48.75 | -29 | 6 | |
-7 | 49 | 35 | -26 | 6 | |
-6.5 | 63.375 | 22.75 | -23 | 6 | |
-6 | 72 | 12 | -20 | 6 | |
-5.5 | 75.625 | 2.75 | -17 | 6 | |
-5.334 | 75.8518 | 0 | -16 | 6 | Hochpunkt H(-5.33|75.85) |
-5 | 75 | -5 | -14 | 6 | |
-4.5 | 70.875 | -11.25 | -11 | 6 | |
-4 | 64 | -16 | -8 | 6 | |
-3.5 | 55.125 | -19.25 | -5 | 6 | |
-3 | 45 | -21 | -2 | 6 | |
-2.666 | 37.9259 | -21.33 | 0 | 6 | Wendepunkt W(-2.67|37.93) |
-2.5 | 34.375 | -21.25 | 1 | 6 | |
-2 | 24 | -20 | 4 | 6 | |
-1.5 | 14.625 | -17.25 | 7 | 6 | |
-1 | 7 | -13 | 10 | 6 | |
-0.5 | 1.875 | -7.25 | 13 | 6 | |
0 | 0 | 0 | 16 | 6 | Nullstelle N(0|0) = Schnittpunkt Sy(0|0) = Tiefpunkt T(0|0) |
0.5 | 2.125 | 8.75 | 19 | 6 | |
1 | 9 | 19 | 22 | 6 | |
1.5 | 21.375 | 30.75 | 25 | 6 | |
2 | 40 | 44 | 28 | 6 | |
2.5 | 65.625 | 58.75 | 31 | 6 | |
3 | 99 | 75 | 34 | 6 | |
3.5 | 140.875 | 92.75 | 37 | 6 | |
4 | 192 | 112 | 40 | 6 | |
4.5 | 253.125 | 132.75 | 43 | 6 | |
5 | 325 | 155 | 46 | 6 | |
5.5 | 408.375 | 178.75 | 49 | 6 | |
6 | 504 | 204 | 52 | 6 | |
6.5 | 612.625 | 230.75 | 55 | 6 | |
7 | 735 | 259 | 58 | 6 | |
7.5 | 871.875 | 288.75 | 61 | 6 | |
8 | 1024 | 320 | 64 | 6 | |
8.5 | 1192.125 | 352.75 | 67 | 6 | |
9 | 1377 | 387 | 70 | 6 | |
9.5 | 1579.375 | 422.75 | 73 | 6 | |
10 | 1800 | 460 | 76 | 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