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Funktion: f(x) = 3·e-0.2x-5·e0.5x, 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 | 22.1335 | -4.45 | 0.88 | -0.18 | |
| -9.5 | 20.0144 | -4.03 | 0.79 | -0.17 | |
| -9 | 18.0934 | -3.66 | 0.71 | -0.15 | |
| -8.5 | 16.3505 | -3.32 | 0.64 | -0.14 | |
| -8 | 14.7675 | -3.02 | 0.57 | -0.13 | |
| -7.5 | 13.3275 | -2.75 | 0.51 | -0.12 | |
| -7 | 12.0146 | -2.51 | 0.45 | -0.12 | |
| -6.5 | 10.814 | -2.3 | 0.39 | -0.11 | |
| -6 | 9.7114 | -2.12 | 0.34 | -0.11 | |
| -5.5 | 8.6929 | -1.96 | 0.28 | -0.11 | |
| -5 | 7.7444 | -1.84 | 0.22 | -0.12 | |
| -4.5 | 6.8518 | -1.74 | 0.16 | -0.13 | |
| -4 | 5.9999 | -1.67 | 0.1 | -0.14 | |
| -3.5 | 5.1724 | -1.64 | 0.02 | -0.16 | |
| -3.35 | 4.9262 | -1.64 | 0 | -0.16 | Wendepunkt W(-3.35|4.93) |
| -3 | 4.3507 | -1.65 | -0.06 | -0.18 | |
| -2.5 | 3.5136 | -1.71 | -0.16 | -0.22 | |
| -2 | 2.6361 | -1.81 | -0.28 | -0.27 | |
| -1.5 | 1.6877 | -1.99 | -0.43 | -0.33 | |
| -1 | 0.6316 | -2.25 | -0.61 | -0.41 | |
| -0.73 | 0 | -2.43 | -0.73 | -0.46 | Nullstelle N(-0.73|0) |
| -0.5 | -0.5785 | -2.61 | -0.84 | -0.51 | |
| 0 | -2 | -3.1 | -1.13 | -0.65 | Schnittpunkt Sy(0|-2) |
| 0.5 | -3.7056 | -3.75 | -1.5 | -0.83 | |
| 1 | -5.7874 | -4.61 | -1.96 | -1.05 | |
| 1.5 | -8.3625 | -5.74 | -2.56 | -1.34 | |
| 2 | -11.5804 | -7.2 | -3.32 | -1.72 | |
| 2.5 | -15.6321 | -9.09 | -4.29 | -2.2 | |
| 3 | -20.762 | -11.53 | -5.54 | -2.82 | |
| 3.5 | -27.2833 | -14.68 | -7.13 | -3.62 | |
| 4 | -35.5973 | -18.74 | -9.18 | -4.64 | |
| 4.5 | -46.219 | -23.96 | -11.81 | -5.95 | |
| 5 | -59.8088 | -30.68 | -15.18 | -7.64 | |
| 5.5 | -77.2145 | -39.31 | -19.51 | -9.81 | |
| 6 | -99.5241 | -50.39 | -25.07 | -12.59 | |
| 6.5 | -128.1341 | -64.64 | -32.21 | -16.17 | |
| 7 | -164.8375 | -82.94 | -41.36 | -20.75 | |
| 7.5 | -211.936 | -106.44 | -53.12 | -26.65 | |
| 8 | -272.3851 | -136.62 | -68.22 | -34.21 | |
| 8.5 | -349.979 | -175.37 | -87.61 | -43.93 | |
| 9 | -449.5898 | -225.14 | -112.5 | -56.41 | |
| 9.5 | -577.4727 | -289.05 | -144.46 | -72.42 | |
| 10 | -741.6598 | -371.12 | -185.5 | -92.99 | |
| 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