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Funktion: f(x) = -x4/16, Df = R, Wf = (-∞ 0], Potenzfunktion 4. Grades, nach unten geöffnet, Funktion achsensymmetrisch zur Senkrechten x = 0, x -> -∞: f(x) -> -∞, x -> +∞: f(x) -> -∞ ->
| Wertetabelle: | |||||
| x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
| -10 | -625 | 250 | -75 | 15 | |
| -9.5 | -509.0664 | 214.34 | -67.69 | 14.25 | |
| -9 | -410.0625 | 182.25 | -60.75 | 13.5 | |
| -8.5 | -326.2539 | 153.53 | -54.19 | 12.75 | |
| -8 | -256 | 128 | -48 | 12 | |
| -7.5 | -197.7539 | 105.47 | -42.19 | 11.25 | |
| -7 | -150.0625 | 85.75 | -36.75 | 10.5 | |
| -6.5 | -111.5664 | 68.66 | -31.69 | 9.75 | |
| -6 | -81 | 54 | -27 | 9 | |
| -5.5 | -57.1914 | 41.59 | -22.69 | 8.25 | |
| -5 | -39.0625 | 31.25 | -18.75 | 7.5 | |
| -4.5 | -25.6289 | 22.78 | -15.19 | 6.75 | |
| -4 | -16 | 16 | -12 | 6 | |
| -3.5 | -9.3789 | 10.72 | -9.19 | 5.25 | |
| -3 | -5.0625 | 6.75 | -6.75 | 4.5 | |
| -2.5 | -2.4414 | 3.91 | -4.69 | 3.75 | |
| -2 | -1 | 2 | -3 | 3 | |
| -1.5 | -0.3164 | 0.84 | -1.69 | 2.25 | |
| -1 | -0.0625 | 0.25 | -0.75 | 1.5 | |
| -0.5 | -0.0039 | 0.03 | -0.19 | 0.75 | |
| 0 | 0 | 0 | 0 | 0 | Nullstelle N(0|0) = Schnittpunkt Sy(0|0) = Hochpunkt H(0|0) |
| 0.5 | -0.0039 | -0.03 | -0.19 | -0.75 | |
| 1 | -0.0625 | -0.25 | -0.75 | -1.5 | |
| 1.5 | -0.3164 | -0.84 | -1.69 | -2.25 | |
| 2 | -1 | -2 | -3 | -3 | |
| 2.5 | -2.4414 | -3.91 | -4.69 | -3.75 | |
| 3 | -5.0625 | -6.75 | -6.75 | -4.5 | |
| 3.5 | -9.3789 | -10.72 | -9.19 | -5.25 | |
| 4 | -16 | -16 | -12 | -6 | |
| 4.5 | -25.6289 | -22.78 | -15.19 | -6.75 | |
| 5 | -39.0625 | -31.25 | -18.75 | -7.5 | |
| 5.5 | -57.1914 | -41.59 | -22.69 | -8.25 | |
| 6 | -81 | -54 | -27 | -9 | |
| 6.5 | -111.5664 | -68.66 | -31.69 | -9.75 | |
| 7 | -150.0625 | -85.75 | -36.75 | -10.5 | |
| 7.5 | -197.7539 | -105.47 | -42.19 | -11.25 | |
| 8 | -256 | -128 | -48 | -12 | |
| 8.5 | -326.2539 | -153.53 | -54.19 | -12.75 | |
| 9 | -410.0625 | -182.25 | -60.75 | -13.5 | |
| 9.5 | -509.0664 | -214.34 | -67.69 | -14.25 | |
| 10 | -625 | -250 | -75 | -15 | |
| 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, N = Nullstelle, P = Polstelle, R = reelle Zahlen, T = Tiefpunkt, W = Wendepunkt, WS = Sattelpunkt, Wf = Wertebereich, {.} = ein-/mehrelementige Menge, [.; .] = abgeschlossenes Intervall, (.; .) = offenes Intervall, [.; .), (.; .] = halboffenes Intervall, ∞ = unendlich.
Bearbeiter: Michael Buhlmann