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Funktion: f(x) = -2·e-0.2x+4-3·e0.4x-3, Df = R, Wf = (-∞; -22.9079], reelle Funktion, x -> -∞: f(x) -> -∞, x -> +∞: f(x) -> -∞ ->
| Wertetabelle: | |||||
| x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
| -20 | -5961.916 | 1192.38 | -238.48 | 47.69 | |
| -19.5 | -5394.5647 | 1078.91 | -215.78 | 43.15 | |
| -19 | -4881.204 | 976.24 | -195.25 | 39.04 | |
| -18.5 | -4416.6961 | 883.34 | -176.67 | 35.33 | |
| -18 | -3996.3919 | 799.28 | -159.86 | 31.97 | |
| -17.5 | -3616.085 | 723.22 | -144.64 | 28.92 | |
| -17 | -3271.969 | 654.39 | -130.88 | 26.17 | |
| -16.5 | -2960.6001 | 592.12 | -118.42 | 23.68 | |
| -16 | -2678.8618 | 535.77 | -107.15 | 21.43 | |
| -15.5 | -2423.9345 | 484.79 | -96.96 | 19.39 | |
| -15 | -2193.2667 | 438.65 | -87.73 | 17.54 | |
| -14.5 | -1984.5499 | 396.91 | -79.38 | 15.87 | |
| -14 | -1795.6951 | 359.14 | -71.83 | 14.36 | |
| -13.5 | -1624.8123 | 324.96 | -64.99 | 13 | |
| -13 | -1470.1912 | 294.04 | -58.81 | 11.76 | |
| -12.5 | -1330.2843 | 266.06 | -53.21 | 10.64 | |
| -12 | -1203.6913 | 240.74 | -48.15 | 9.63 | |
| -11.5 | -1089.1453 | 217.83 | -43.57 | 8.71 | |
| -11 | -985.4999 | 197.1 | -39.42 | 7.88 | |
| -10.5 | -891.7178 | 178.34 | -35.67 | 7.13 | |
| -10 | -806.8603 | 161.37 | -32.27 | 6.45 | |
| -9.5 | -730.0783 | 146.01 | -29.2 | 5.84 | |
| -9 | -660.6032 | 132.12 | -26.42 | 5.28 | |
| -8.5 | -597.7398 | 119.54 | -23.91 | 4.78 | |
| -8 | -540.8589 | 108.17 | -21.64 | 4.33 | |
| -7.5 | -489.3913 | 97.87 | -19.58 | 3.91 | |
| -7 | -442.8219 | 88.56 | -17.71 | 3.54 | |
| -6.5 | -400.6847 | 80.13 | -16.03 | 3.2 | |
| -6 | -362.558 | 72.5 | -14.5 | 2.9 | |
| -5.5 | -328.0604 | 65.6 | -13.12 | 2.62 | |
| -5 | -296.8465 | 59.36 | -11.88 | 2.37 | |
| -4.5 | -268.6042 | 53.71 | -10.75 | 2.15 | |
| -4 | -243.051 | 48.59 | -9.73 | 1.94 | |
| -3.5 | -219.9312 | 43.96 | -8.8 | 1.76 | |
| -3 | -199.0136 | 39.78 | -7.97 | 1.59 | |
| -2.5 | -180.0892 | 35.98 | -7.21 | 1.44 | |
| -2 | -162.9688 | 32.55 | -6.53 | 1.3 | |
| -1.5 | -147.4816 | 29.45 | -5.91 | 1.17 | |
| -1 | -133.4728 | 26.63 | -5.35 | 1.06 | |
| -0.5 | -120.8029 | 24.09 | -4.85 | 0.96 | |
| 0 | -109.3457 | 21.78 | -4.39 | 0.86 | Schnittpunkt Sy(0|-109.35) |
| 0.5 | -98.9873 | 19.69 | -3.98 | 0.78 | |
| 1 | -89.6252 | 17.79 | -3.61 | 0.7 | |
| 1.5 | -81.1668 | 16.07 | -3.28 | 0.63 | |
| 2 | -73.5289 | 14.51 | -2.98 | 0.56 | |
| 2.5 | -66.6369 | 13.08 | -2.71 | 0.5 | |
| 3 | -60.4241 | 11.79 | -2.48 | 0.45 | |
| 3.5 | -54.831 | 10.6 | -2.27 | 0.39 | |
| 4 | -49.8049 | 9.52 | -2.08 | 0.35 | |
| 4.5 | -45.2995 | 8.52 | -1.92 | 0.3 | |
| 5 | -41.2747 | 7.59 | -1.78 | 0.25 | |
| 5.5 | -37.6963 | 6.73 | -1.67 | 0.2 | |
| 6 | -34.5357 | 5.92 | -1.58 | 0.16 | |
| 6.5 | -31.7704 | 5.15 | -1.51 | 0.11 | |
| 7 | -29.3837 | 4.4 | -1.47 | 0.06 | |
| 7.5 | -27.365 | 3.67 | -1.45 | 0 | |
| 8 | -25.7106 | 2.94 | -1.47 | -0.06 | |
| 8.5 | -24.4238 | 2.2 | -1.51 | -0.13 | |
| 9 | -23.5164 | 1.42 | -1.6 | -0.21 | |
| 9.5 | -23.009 | 0.6 | -1.72 | -0.3 | |
| 9.834 | -22.9079 | 0 | -1.83 | -0.37 | Hochpunkt H(9.83|-22.91) |
| 10 | -22.933 | -0.31 | -1.9 | -0.4 | |
| 10.5 | -23.3321 | -1.31 | -2.13 | -0.53 | |
| 11 | -24.2649 | -2.45 | -2.43 | -0.68 | |
| 11.5 | -25.807 | -3.75 | -2.82 | -0.86 | |
| 12 | -28.055 | -5.28 | -3.3 | -1.08 | |
| 12.5 | -31.1305 | -7.07 | -3.91 | -1.35 | |
| 13 | -35.1854 | -9.21 | -4.66 | -1.67 | |
| 13.5 | -40.4081 | -11.76 | -5.58 | -2.06 | |
| 14 | -47.0314 | -14.83 | -6.73 | -2.53 | |
| 14.5 | -55.3423 | -18.53 | -8.13 | -3.11 | |
| 15 | -65.6932 | -23.02 | -9.86 | -3.81 | |
| 15.5 | -78.5168 | -28.46 | -11.97 | -4.67 | |
| 16 | -94.3434 | -35.07 | -14.56 | -5.72 | |
| 16.5 | -113.8222 | -43.11 | -17.73 | -7 | |
| 17 | -137.7478 | -52.91 | -21.6 | -8.56 | |
| 17.5 | -167.0919 | -64.86 | -26.34 | -10.46 | |
| 18 | -203.0426 | -79.43 | -32.13 | -12.79 | |
| 18.5 | -247.0523 | -97.2 | -39.2 | -15.62 | |
| 19 | -300.8958 | -118.89 | -47.85 | -19.09 | |
| 19.5 | -366.7416 | -145.37 | -58.41 | -23.32 | |
| 20 | -447.2395 | -177.7 | -71.32 | -28.49 | |
| 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