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Funktion: f(x) = 1+e0.5x, Df = R, Wf = (1; +∞), reelle Funktion, x -> -∞: f(x) -> 1 = y als Grenzkurve, x -> +∞: f(x) -> +∞ ->
Wertetabelle: | |||||
x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
-8 | 1.0183 | 0.01 | 0 | 0 | |
-7.5 | 1.0235 | 0.01 | 0.01 | 0 | |
-7 | 1.0302 | 0.02 | 0.01 | 0 | |
-6.5 | 1.0388 | 0.02 | 0.01 | 0 | |
-6 | 1.0498 | 0.02 | 0.01 | 0.01 | |
-5.5 | 1.0639 | 0.03 | 0.02 | 0.01 | |
-5 | 1.0821 | 0.04 | 0.02 | 0.01 | |
-4.5 | 1.1054 | 0.05 | 0.03 | 0.01 | |
-4 | 1.1353 | 0.07 | 0.03 | 0.02 | |
-3.5 | 1.1738 | 0.09 | 0.04 | 0.02 | |
-3 | 1.2231 | 0.11 | 0.06 | 0.03 | |
-2.5 | 1.2865 | 0.14 | 0.07 | 0.04 | |
-2 | 1.3679 | 0.18 | 0.09 | 0.05 | |
-1.5 | 1.4724 | 0.24 | 0.12 | 0.06 | |
-1 | 1.6065 | 0.3 | 0.15 | 0.08 | |
-0.5 | 1.7788 | 0.39 | 0.19 | 0.1 | |
0 | 2 | 0.5 | 0.25 | 0.13 | Schnittpunkt Sy(0|2) |
0.5 | 2.284 | 0.64 | 0.32 | 0.16 | |
1 | 2.6487 | 0.82 | 0.41 | 0.21 | |
1.5 | 3.117 | 1.06 | 0.53 | 0.27 | |
2 | 3.7183 | 1.36 | 0.68 | 0.34 | |
2.5 | 4.4903 | 1.75 | 0.87 | 0.44 | |
3 | 5.4817 | 2.24 | 1.12 | 0.56 | |
3.5 | 6.7546 | 2.88 | 1.44 | 0.72 | |
4 | 8.3891 | 3.69 | 1.85 | 0.93 | |
4.5 | 10.4877 | 4.74 | 2.37 | 1.19 | |
5 | 13.1825 | 6.09 | 3.05 | 1.53 | |
5.5 | 16.6426 | 7.82 | 3.91 | 1.96 | |
6 | 21.0855 | 10.04 | 5.02 | 2.52 | |
6.5 | 26.7903 | 12.9 | 6.45 | 3.23 | |
7 | 34.1155 | 16.56 | 8.28 | 4.15 | |
7.5 | 43.5211 | 21.26 | 10.63 | 5.33 | |
8 | 55.5982 | 27.3 | 13.65 | 6.84 | |
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