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Funktion: f(x) = -1.5·e-x+5, Df = R, Wf = (-∞; 5), reelle Funktion, x -> -∞: f(x) -> -∞, x -> +∞: f(x) -> 5 = y als Grenzkurve ->
Wertetabelle: | |||||
x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
-8 | -4466.437 | 4471.51 | -4471.47 | 4449.19 | |
-7.5 | -2707.0636 | 2712.11 | -2712.09 | 2698.57 | |
-7 | -1639.9497 | 1644.98 | -1644.96 | 1636.77 | |
-6.5 | -992.7124 | 997.73 | -997.72 | 992.75 | |
-6 | -600.1432 | 605.15 | -605.15 | 602.13 | |
-5.5 | -362.0379 | 367.04 | -367.04 | 365.21 | |
-5 | -217.6197 | 222.62 | -222.62 | 221.51 | |
-4.5 | -130.0257 | 135.03 | -135.03 | 134.35 | |
-4 | -76.8972 | 81.9 | -81.9 | 81.49 | |
-3.5 | -44.6732 | 49.67 | -49.67 | 49.43 | |
-3 | -25.1283 | 30.13 | -30.13 | 29.98 | |
-2.5 | -13.2737 | 18.27 | -18.27 | 18.18 | |
-2 | -6.0836 | 11.08 | -11.08 | 11.03 | |
-1.5 | -1.7225 | 6.72 | -6.72 | 6.69 | |
-1.21 | 0 | 5.03 | -5.03 | 5.01 | Nullstelle N(-1.21|0) |
-1 | 0.9226 | 4.08 | -4.08 | 4.06 | |
-0.5 | 2.5269 | 2.47 | -2.47 | 2.46 | |
0 | 3.5 | 1.5 | -1.5 | 1.49 | Schnittpunkt Sy(0|3.5) |
0.5 | 4.0902 | 0.91 | -0.91 | 0.91 | |
1 | 4.4482 | 0.55 | -0.55 | 0.55 | |
1.5 | 4.6653 | 0.33 | -0.33 | 0.33 | |
2 | 4.797 | 0.2 | -0.2 | 0.2 | |
2.5 | 4.8769 | 0.12 | -0.12 | 0.12 | |
3 | 4.9253 | 0.07 | -0.07 | 0.07 | |
3.5 | 4.9547 | 0.05 | -0.05 | 0.05 | |
4 | 4.9725 | 0.03 | -0.03 | 0.03 | |
4.5 | 4.9833 | 0.02 | -0.02 | 0.02 | |
5 | 4.9899 | 0.01 | -0.01 | 0.01 | |
5.5 | 4.9939 | 0.01 | -0.01 | 0.01 | |
6 | 4.9963 | 0 | 0 | 0 | |
6.5 | 4.9977 | 0 | 0 | 0 | |
7 | 4.9986 | 0 | 0 | 0 | |
7.5 | 4.9992 | 0 | 0 | 0 | |
8 | 4.9995 | 0 | 0 | 0 | |
Graph: | |||||
Graph(en) der Asymptote(n), Grenzkurve(n).
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