, Df = R\{-3; 0}, Wf = R, reelle Funktion, x -> -∞: f(x) -> +∞, x -> +∞: f(x) -> +∞ ->www.michael-buhlmann.de
Funktion: f(x) = , Df = R\{-3; 0}, Wf = R, reelle Funktion, x -> -∞: f(x) -> +∞, x -> +∞: f(x) -> +∞ ->
| Wertetabelle: | |||||
| x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
| -20 | 2866.5716 | -306.07 | 18.28 | -0.18 | |
| -19.5 | 2715.8184 | -296.95 | 18.19 | -0.19 | |
| -19 | 2569.6134 | -287.88 | 18.1 | -0.19 | |
| -18.5 | 2427.9329 | -278.85 | 18 | -0.19 | |
| -18 | 2290.7531 | -269.88 | 17.9 | -0.2 | |
| -17.5 | 2158.0494 | -260.95 | 17.8 | -0.2 | |
| -17 | 2029.7967 | -252.07 | 17.7 | -0.21 | |
| -16.5 | 1905.9697 | -243.25 | 17.6 | -0.21 | |
| -16 | 1786.5421 | -234.47 | 17.49 | -0.22 | |
| -15.5 | 1671.4873 | -225.75 | 17.38 | -0.22 | |
| -15 | 1560.7782 | -217.09 | 17.27 | -0.22 | |
| -14.5 | 1454.3872 | -208.48 | 17.16 | -0.23 | |
| -14 | 1352.2861 | -199.93 | 17.05 | -0.23 | |
| -13.5 | 1254.4462 | -191.44 | 16.93 | -0.23 | |
| -13 | 1160.8387 | -183 | 16.81 | -0.23 | |
| -12.5 | 1071.4345 | -174.62 | 16.7 | -0.23 | |
| -12 | 986.2042 | -166.31 | 16.58 | -0.23 | |
| -11.5 | 905.1187 | -158.05 | 16.47 | -0.23 | |
| -11 | 828.1497 | -149.84 | 16.36 | -0.21 | |
| -10.5 | 755.2695 | -141.69 | 16.25 | -0.19 | |
| -10 | 686.4529 | -133.59 | 16.16 | -0.16 | |
| -9.5 | 621.6773 | -125.52 | 16.09 | -0.11 | |
| -9 | 560.9256 | -117.49 | 16.05 | -0.03 | |
| -8.5 | 504.1884 | -109.46 | 16.07 | 0.09 | |
| -8 | 451.4696 | -101.41 | 16.16 | 0.31 | |
| -7.5 | 402.7943 | -93.27 | 16.4 | 0.67 | |
| -7 | 358.2236 | -84.97 | 16.88 | 1.32 | |
| -6.5 | 317.8821 | -76.32 | 17.82 | 2.57 | |
| -6 | 282.0134 | -67 | 19.67 | 5.17 | |
| -5.5 | 251.102 | -56.32 | 23.55 | 11.29 | |
| -5 | 226.1797 | -42.62 | 32.67 | 28.4 | |
| -4.5 | 209.7454 | -21 | 58.81 | 91.17 | |
| -4.222 | 206.5803 | 0 | 97.54 | 207.99 | Tiefpunkt T(-4.22|206.58) |
| -4 | 209.4457 | 28.36 | 167.27 | 465.02 | |
| -3.5 | 263.8488 | 266.55 | 1249.42 | 7482.31 | |
| -3 | Infinity | Infinity | Infinity | Infinity | Senkrechte Asymptote/Pol x = -3 mit Vorzeichenwechsel: x -> -3-: f(x) -> +∞, x -> -3+: f(x) -> -∞ |
| -2.5 | -82.2682 | 278.26 | -1226.03 | 7363.25 | |
| -2 | -19.0904 | 51.73 | -144.09 | 460.73 | |
| -1.5 | -4.8246 | 13.87 | -36.02 | 89.71 | |
| -1 | -1 | 3.5 | -10.5 | 26.69 | |
| -0.5 | -0.1307 | 0.64 | -2.45 | 8.38 | |
| 0 | - | - | - | - | Lücke L(0|0) |
| 0.5 | -0.1924 | -0.67 | -0.52 | 4.36 | |
| 0.616 | -0.2725 | -0.7 | -0.01 | 4.48 | Wendepunkt W(0.62|-0.27) |
| 1 | -0.5 | -0.37 | 1.69 | 4.23 | |
| 1.18 | -0.5361 | 0 | 2.43 | 3.99 | Tiefpunkt T(1.18|-0.54) |
| 1.5 | -0.3918 | 0.97 | 3.64 | 3.55 | |
| 1.762 | 0 | 2.04 | 4.52 | 3.2 | Nullstelle N(1.76|0) |
| 2 | 0.6181 | 3.2 | 5.25 | 2.91 | |
| 2.5 | 2.9335 | 6.17 | 6.57 | 2.41 | |
| 3 | 6.8875 | 9.74 | 7.68 | 2.02 | |
| 3.5 | 12.7576 | 13.82 | 8.61 | 1.72 | |
| 4 | 20.778 | 18.33 | 9.41 | 1.49 | |
| 4.5 | 31.1491 | 23.21 | 10.11 | 1.3 | |
| 5 | 44.0449 | 28.42 | 10.72 | 1.15 | |
| 5.5 | 59.6182 | 33.92 | 11.26 | 1.02 | |
| 6 | 78.0045 | 39.67 | 11.74 | 0.92 | |
| 6.5 | 99.325 | 45.65 | 12.18 | 0.83 | |
| 7 | 123.6894 | 51.84 | 12.58 | 0.76 | |
| 7.5 | 151.1976 | 58.22 | 12.94 | 0.7 | |
| 8 | 181.9407 | 64.78 | 13.28 | 0.65 | |
| 8.5 | 216.0032 | 71.5 | 13.59 | 0.6 | |
| 9 | 253.4628 | 78.37 | 13.88 | 0.56 | |
| 9.5 | 294.3922 | 85.37 | 14.15 | 0.52 | |
| 10 | 338.8592 | 92.51 | 14.41 | 0.49 | |
| 10.5 | 386.9275 | 99.78 | 14.65 | 0.47 | |
| 11 | 438.6569 | 107.16 | 14.87 | 0.44 | |
| 11.5 | 494.1041 | 114.65 | 15.09 | 0.42 | |
| 12 | 553.3225 | 122.24 | 15.29 | 0.4 | |
| 12.5 | 616.3631 | 129.94 | 15.48 | 0.38 | |
| 13 | 683.2742 | 137.72 | 15.67 | 0.36 | |
| 13.5 | 754.1021 | 145.6 | 15.84 | 0.35 | |
| 14 | 828.891 | 153.57 | 16.01 | 0.33 | |
| 14.5 | 907.683 | 161.61 | 16.18 | 0.32 | |
| 15 | 990.5188 | 169.74 | 16.33 | 0.31 | |
| 15.5 | 1077.4374 | 177.95 | 16.48 | 0.29 | |
| 16 | 1168.4761 | 186.22 | 16.63 | 0.28 | |
| 16.5 | 1263.6713 | 194.57 | 16.77 | 0.27 | |
| 17 | 1363.0577 | 202.99 | 16.9 | 0.26 | |
| 17.5 | 1466.6691 | 211.47 | 17.03 | 0.26 | |
| 18 | 1574.5379 | 220.02 | 17.16 | 0.25 | |
| 18.5 | 1686.6958 | 228.63 | 17.28 | 0.24 | |
| 19 | 1803.1734 | 237.29 | 17.4 | 0.23 | |
| 19.5 | 1924.0002 | 246.02 | 17.51 | 0.23 | |
| 20 | 2049.2051 | 254.81 | 17.62 | 0.22 | |
| Graph: | |||||
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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