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Funktion: f(x) = x3 + 0.5·x2 + x + 5, Df = R, Wf = R, Polynom 3. Grades, Funktion punktsymmetrisch zum Punkt W(-0.17|4.84), x -> -∞: f(x) -> -∞, x -> +∞: f(x) -> +∞ ->
Wertetabelle: | |||||
x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
-10 | -955 | 291 | -59 | 6 | |
-9.5 | -816.75 | 262.25 | -56 | 6 | |
-9 | -692.5 | 235 | -53 | 6 | |
-8.5 | -581.5 | 209.25 | -50 | 6 | |
-8 | -483 | 185 | -47 | 6 | |
-7.5 | -396.25 | 162.25 | -44 | 6 | |
-7 | -320.5 | 141 | -41 | 6 | |
-6.5 | -255 | 121.25 | -38 | 6 | |
-6 | -199 | 103 | -35 | 6 | |
-5.5 | -151.75 | 86.25 | -32 | 6 | |
-5 | -112.5 | 71 | -29 | 6 | |
-4.5 | -80.5 | 57.25 | -26 | 6 | |
-4 | -55 | 45 | -23 | 6 | |
-3.5 | -35.25 | 34.25 | -20 | 6 | |
-3 | -20.5 | 25 | -17 | 6 | |
-2.5 | -10 | 17.25 | -14 | 6 | |
-2 | -3 | 11 | -11 | 6 | |
-1.679 | 0 | 7.78 | -9.07 | 6 | Nullstelle N(-1.68|0) |
-1.5 | 1.25 | 6.25 | -8 | 6 | |
-1 | 3.5 | 3 | -5 | 6 | |
-0.5 | 4.5 | 1.25 | -2 | 6 | |
-0.167 | 4.8423 | 0.92 | 0 | 6 | Wendepunkt W(-0.17|4.84) |
0 | 5 | 1 | 1 | 6 | Schnittpunkt Sy(0|5) |
0.5 | 5.75 | 2.25 | 4 | 6 | |
1 | 7.5 | 5 | 7 | 6 | |
1.5 | 11 | 9.25 | 10 | 6 | |
2 | 17 | 15 | 13 | 6 | |
2.5 | 26.25 | 22.25 | 16 | 6 | |
3 | 39.5 | 31 | 19 | 6 | |
3.5 | 57.5 | 41.25 | 22 | 6 | |
4 | 81 | 53 | 25 | 6 | |
4.5 | 110.75 | 66.25 | 28 | 6 | |
5 | 147.5 | 81 | 31 | 6 | |
5.5 | 192 | 97.25 | 34 | 6 | |
6 | 245 | 115 | 37 | 6 | |
6.5 | 307.25 | 134.25 | 40 | 6 | |
7 | 379.5 | 155 | 43 | 6 | |
7.5 | 462.5 | 177.25 | 46 | 6 | |
8 | 557 | 201 | 49 | 6 | |
8.5 | 663.75 | 226.25 | 52 | 6 | |
9 | 783.5 | 253 | 55 | 6 | |
9.5 | 917 | 281.25 | 58 | 6 | |
10 | 1065 | 311 | 61 | 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