, Df = R\{-0.57}, Wf = R, reelle Funktion, x -> -∞: f(x) -> +∞, x -> +∞: -> f(x) -> 1 = y als Grenzkurvewww.michael-buhlmann.de
Funktion: f(x) = , Df = R\{-0.57}, Wf = R, reelle Funktion, x -> -∞: f(x) -> +∞, x -> +∞: -> f(x) -> 1 = y als Grenzkurve
| Wertetabelle: | |||||
| x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
| -15 | 3375.0001 | -675 | 90 | -6 | |
| -14.5 | 3048.6251 | -630.75 | 87 | -6 | |
| -14 | 2744.0002 | -588 | 84 | -6 | |
| -13.5 | 2460.3752 | -546.75 | 81 | -6 | |
| -13 | 2197.0004 | -507 | 78 | -6 | |
| -12.5 | 1953.1256 | -468.75 | 75 | -6 | |
| -12 | 1728.0009 | -432 | 72 | -6 | |
| -11.5 | 1520.8763 | -396.75 | 69 | -6 | |
| -11 | 1331.002 | -363 | 66 | -6 | |
| -10.5 | 1157.628 | -330.75 | 63 | -6 | |
| -10 | 1000.0045 | -300 | 60 | -6 | |
| -9.5 | 857.3817 | -270.74 | 57 | -6 | |
| -9 | 729.01 | -242.99 | 54.01 | -6 | |
| -8.5 | 614.1397 | -216.74 | 51.01 | -5.99 | |
| -8 | 512.0214 | -191.98 | 48.01 | -5.99 | |
| -7.5 | 421.906 | -168.73 | 45.02 | -5.99 | |
| -7 | 343.0446 | -146.97 | 42.02 | -5.99 | |
| -6.5 | 274.6883 | -126.71 | 39.03 | -5.99 | |
| -6 | 216.0889 | -107.94 | 36.03 | -5.99 | |
| -5.5 | 166.498 | -90.67 | 33.04 | -5.99 | |
| -5 | 125.1673 | -74.9 | 30.05 | -5.99 | |
| -4.5 | 91.348 | -60.63 | 27.05 | -6.01 | |
| -4 | 64.2898 | -47.86 | 24.03 | -6.04 | |
| -3.5 | 43.2394 | -36.6 | 21 | -6.09 | |
| -3 | 27.4388 | -26.86 | 17.94 | -6.17 | |
| -2.5 | 16.1215 | -18.67 | 14.82 | -6.3 | |
| -2 | 8.5081 | -12.05 | 11.61 | -6.62 | |
| -1.5 | 3.79 | -7.12 | 8 | -8.5 | |
| -1.04 | 1.1891 | -4.72 | 0.37 | -42.91 | Wendepunkt W(-1.04|1.19) |
| -1 | 1 | -4.75 | -1.56 | -58.83 | |
| -0.82 | 0 | -6.86 | -31.94 | -477.89 | Nullstelle N(-0.82|0) |
| -0.57 | Infinity | Infinity | Infinity | Infinity | Senkrechte Asymptote/Pol x = -0.57 mit Vorzeichenwechsel: x -> -0.57-: f(x) -> -∞, x -> -0.57+: f(x) -> +∞ |
| -0.5 | 5.1068 | -68.11 | 2002.3 | -68832.93 | |
| 0 | 1 | -1 | 4 | -20.41 | Schnittpunkt Sy(0|1) |
| 0.42 | 0.7677 | -0.37 | 0 | -4.26 | Wendepunkt W(0.42|0.77) |
| 0.5 | 0.7382 | -0.38 | -0.27 | -3.48 | |
| 1 | 0.4621 | -0.81 | -1.22 | -0.61 | |
| 1.42 | 0 | -1.33 | -1.16 | 0.81 | Nullstelle N(1.42|0) |
| 1.5 | -0.0971 | -1.42 | -1.09 | 1.01 | |
| 2 | -0.9171 | -1.8 | -0.38 | 1.68 | |
| 2.22 | -1.3198 | -1.85 | -0.01 | 1.69 | Wendepunkt W(2.22|-1.32) |
| 2.5 | -1.8308 | -1.78 | 0.44 | 1.5 | |
| 3 | -2.6386 | -1.4 | 1.04 | 0.83 | |
| 3.5 | -3.1939 | -0.8 | 1.28 | 0.11 | |
| 4 | -3.437 | -0.18 | 1.19 | -0.41 | |
| 4.15 | -3.4502 | 0 | 1.12 | -0.51 | Tiefpunkt T(4.15|-3.45) |
| 4.5 | -3.3861 | 0.36 | 0.92 | -0.64 | |
| 5 | -3.1066 | 0.73 | 0.59 | -0.66 | |
| 5.5 | -2.6794 | 0.95 | 0.28 | -0.55 | |
| 6 | -2.18 | 1.03 | 0.05 | -0.39 | |
| 6.12 | -2.0564 | 1.03 | 0 | -0.36 | Wendepunkt W(6.12|-2.06) |
| 6.5 | -1.6674 | 1.01 | -0.11 | -0.25 | |
| 7 | -1.1819 | 0.93 | -0.21 | -0.13 | |
| 7.5 | -0.7469 | 0.81 | -0.25 | -0.04 | |
| 8 | -0.3731 | 0.68 | -0.25 | 0.02 | |
| 8.5 | -0.062 | 0.56 | -0.24 | 0.05 | |
| 8.61 | -0.0017 | 0.54 | -0.23 | 0.05 | Nullstelle N(8.61|0) |
| 9 | 0.1901 | 0.45 | -0.21 | 0.06 | |
| 9.5 | 0.39 | 0.35 | -0.18 | 0.06 | |
| 10 | 0.5458 | 0.27 | -0.15 | 0.06 | |
| 10.5 | 0.6651 | 0.21 | -0.12 | 0.05 | |
| 11 | 0.7553 | 0.16 | -0.09 | 0.05 | |
| 11.5 | 0.8227 | 0.12 | -0.07 | 0.04 | |
| 12 | 0.8725 | 0.08 | -0.05 | 0.03 | |
| 12.5 | 0.909 | 0.06 | -0.04 | 0.02 | |
| 13 | 0.9354 | 0.04 | -0.03 | 0.02 | |
| 13.5 | 0.9544 | 0.03 | -0.02 | 0.01 | |
| 14 | 0.968 | 0.02 | -0.02 | 0.01 | |
| 14.5 | 0.9777 | 0.02 | -0.01 | 0.01 | |
| 15 | 0.9845 | 0.01 | -0.01 | 0.01 | |
| Graph: | |||||
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Graph(en) der Asymptote(n), Grenzkurve(n).
Abkürzungen: Df = (maximaler) Definitionsbereich, f(x) = Funktion, f'(x) = 1. Ableitung, f''(x) = 2. Ableitung, f'''(x) = 3. Ableitung, H = Hochpunkt, L = Lücke, N = Nullstelle, P = Polstelle, R = reelle Zahlen, S = Sprungstelle, T = Tiefpunkt, W = Wendepunkt, WS = Sattelpunkt, Wf = Wertebereich, {.} = ein-/mehrelementige Menge, [.; .] = abgeschlossenes Intervall, (.; .) = offenes Intervall, [.; .), (.; .] = halboffenes Intervall, ∞ = unendlich.
Bearbeiter: Michael Buhlmann