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Funktion: f(x) = e0.5x+1-e-x+2, Df = R, Wf = R, reelle Funktion, x -> -∞: f(x) -> -∞, x -> +∞: f(x) -> +∞ ->
| Wertetabelle: | |||||
| x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
| -10 | -162754.7731 | 162754.91 | -162754.84 | 162592.16 | |
| -9.5 | -98715.7475 | 98715.85 | -98715.8 | 98617.14 | |
| -9 | -59874.1115 | 59874.2 | -59874.15 | 59814.32 | |
| -8.5 | -36315.4639 | 36315.55 | -36315.51 | 36279.22 | |
| -8 | -22026.416 | 22026.51 | -22026.46 | 22004.48 | |
| -7.5 | -13359.6629 | 13359.77 | -13359.72 | 13346.39 | |
| -7 | -8103.0018 | 8103.13 | -8103.07 | 8095 | |
| -6.5 | -4914.6634 | 4914.82 | -4914.74 | 4909.87 | |
| -6 | -2980.8227 | 2981.03 | -2980.93 | 2978 | |
| -5.5 | -1807.8686 | 1808.13 | -1808 | 1806.26 | |
| -5 | -1096.41 | 1096.75 | -1096.58 | 1095.57 | |
| -4.5 | -664.8551 | 665.29 | -665.07 | 664.51 | |
| -4 | -403.0609 | 403.61 | -403.34 | 403.07 | |
| -3.5 | -244.2196 | 244.93 | -244.57 | 244.51 | |
| -3 | -147.8066 | 148.72 | -148.26 | 148.34 | |
| -2.5 | -89.2383 | 90.41 | -89.82 | 90.02 | |
| -2 | -53.5982 | 55.1 | -54.35 | 54.67 | |
| -1.5 | -31.8314 | 33.76 | -32.79 | 33.24 | |
| -1 | -18.4368 | 20.91 | -19.67 | 20.27 | |
| -0.5 | -10.0655 | 13.24 | -11.65 | 12.44 | |
| 0 | -4.6708 | 8.75 | -6.71 | 7.72 | Schnittpunkt Sy(0|-4.67) |
| 0.5 | -0.9913 | 6.23 | -3.61 | 4.91 | |
| 0.666 | 0 | 5.69 | -2.85 | 4.27 | Nullstelle N(0.67|0) |
| 1 | 1.7634 | 4.96 | -1.6 | 3.28 | |
| 1.5 | 4.1059 | 4.53 | -0.21 | 2.37 | |
| 1.59 | 4.5127 | 4.52 | 0 | 2.26 | Wendepunkt W(1.59|4.51) |
| 2 | 6.3891 | 4.69 | 0.85 | 1.92 | |
| 2.5 | 8.8812 | 5.35 | 1.77 | 1.79 | |
| 3 | 11.8146 | 6.46 | 2.68 | 1.89 | |
| 3.5 | 15.4195 | 8.04 | 3.69 | 2.18 | |
| 4 | 19.9502 | 10.18 | 4.89 | 2.65 | |
| 4.5 | 25.7083 | 12.98 | 6.37 | 3.31 | |
| 5 | 33.0657 | 16.61 | 8.23 | 4.19 | |
| 5.5 | 42.4909 | 21.29 | 10.6 | 5.35 | |
| 6 | 54.5798 | 27.32 | 13.63 | 6.85 | |
| 6.5 | 70.0943 | 35.06 | 17.52 | 8.78 | |
| 7 | 90.0104 | 45.02 | 22.5 | 11.26 | |
| 7.5 | 115.5802 | 57.8 | 28.89 | 14.46 | |
| 8 | 148.4107 | 74.21 | 37.1 | 18.56 | |
| 8.5 | 190.5648 | 95.28 | 47.64 | 23.83 | |
| 9 | 244.691 | 122.35 | 61.17 | 30.6 | |
| 9.5 | 314.1901 | 157.1 | 78.55 | 39.29 | |
| 10 | 403.4285 | 201.71 | 100.86 | 50.45 | |
| 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