www.michael-buhlmann.de
Funktion: f(x) = (4-x2)·e-0.5x, Df = R, Wf = (-∞; 0.4463], reelle Funktion, x -> -∞: f(x) -> +∞, x -> +∞: f(x) -> 0 = y als Grenzkurve ->
| Wertetabelle: | |||||
| x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
| -10 | -14247.6633 | 10092.17 | -6827.03 | 4438.34 | |
| -9.5 | -9969.1445 | 7180.73 | -4919.57 | 3229.66 | |
| -9 | -6931.3191 | 5086.01 | -3533.19 | 2344.15 | |
| -8.5 | -4784.6944 | 3584.17 | -2528.19 | 1696.74 | |
| -8 | -3275.889 | 2511.54 | -1801.75 | 1224.44 | |
| -7.5 | -2221.7265 | 1748.69 | -1278.29 | 880.72 | |
| -7 | -1490.1953 | 1208.72 | -902.4 | 631.22 | |
| -6.5 | -986.4805 | 828.52 | -633.48 | 450.61 | |
| -6 | -642.7372 | 562.4 | -441.88 | 320.27 | |
| -5.5 | -410.6191 | 377.38 | -306.01 | 226.52 | |
| -5 | -255.8324 | 249.74 | -210.15 | 159.33 | |
| -4.5 | -154.1757 | 162.48 | -142.91 | 111.37 | |
| -4 | -88.6687 | 103.45 | -96.06 | 77.3 | |
| -3.5 | -47.4755 | 64.02 | -63.66 | 53.21 | |
| -3 | -22.4084 | 38.09 | -41.46 | 36.27 | |
| -2.5 | -7.8533 | 21.38 | -26.4 | 24.44 | |
| -2 | 0 | 10.87 | -16.31 | 16.24 | Nullstelle N(-2|0) |
| -1.5 | 3.7048 | 4.5 | -9.66 | 10.6 | |
| -1 | 4.9462 | 0.82 | -5.36 | 6.77 | |
| -0.83 | 5.0142 | 0 | -4.29 | 5.77 | Hochpunkt H(-0.83|5.01) |
| -0.5 | 4.8151 | -1.12 | -2.65 | 4.19 | |
| 0 | 4 | -2 | -1 | 2.49 | Schnittpunkt Sy(0|4) |
| 0.5 | 2.9205 | -2.24 | -0.05 | 1.38 | |
| 0.53 | 2.8533 | -2.24 | 0 | 1.33 | Wendepunkt W(0.53|2.85) |
| 1 | 1.8196 | -2.12 | 0.45 | 0.68 | |
| 1.5 | 0.8266 | -1.83 | 0.68 | 0.25 | |
| 2 | 0 | -1.47 | 0.74 | 0 | Nullstelle N(2|0) |
| 2.5 | -0.6446 | -1.11 | 0.7 | -0.14 | |
| 3 | -1.1157 | -0.78 | 0.61 | -0.2 | |
| 3.5 | -1.4336 | -0.5 | 0.51 | -0.21 | |
| 4 | -1.624 | -0.27 | 0.41 | -0.2 | |
| 4.5 | -1.7127 | -0.09 | 0.31 | -0.18 | |
| 4.82 | -1.7274 | 0 | 0.25 | -0.16 | Tiefpunkt T(4.82|-1.73) |
| 5 | -1.7238 | 0.04 | 0.23 | -0.15 | |
| 5.5 | -1.6781 | 0.14 | 0.16 | -0.13 | |
| 6 | -1.5932 | 0.2 | 0.1 | -0.1 | |
| 6.5 | -1.4831 | 0.24 | 0.06 | -0.08 | |
| 7 | -1.3589 | 0.26 | 0.02 | -0.06 | |
| 7.46 | -1.2393 | 0.26 | 0 | -0.04 | Wendepunkt W(7.46|-1.24) |
| 7.5 | -1.2288 | 0.26 | 0 | -0.04 | |
| 8 | -1.0989 | 0.26 | -0.02 | -0.03 | |
| 8.5 | -0.9735 | 0.24 | -0.03 | -0.02 | |
| 9 | -0.8554 | 0.23 | -0.04 | -0.01 | |
| 9.5 | -0.7462 | 0.21 | -0.04 | 0 | |
| 10 | -0.6468 | 0.19 | -0.04 | 0 | |
| Graph: | |||||
| |||||
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