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Funktion: f(x) = -x4/4 + 5, Df = R, Wf = (-∞ 5], Potenzfunktion 4. Grades, nach unten geöffnet, entlang der y-Achse nach oben verschoben, 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 | -2495 | 1000 | -300 | 59.99 | |
| -9.5 | -2031.2656 | 857.38 | -270.75 | 56.99 | |
| -9 | -1635.25 | 729 | -243 | 53.99 | |
| -8.5 | -1300.0156 | 614.13 | -216.75 | 50.99 | |
| -8 | -1019 | 512 | -192 | 47.99 | |
| -7.5 | -786.0156 | 421.88 | -168.75 | 44.99 | |
| -7 | -595.25 | 343 | -147 | 41.99 | |
| -6.5 | -441.2656 | 274.63 | -126.75 | 38.99 | |
| -6 | -319 | 216 | -108 | 35.99 | |
| -5.5 | -223.7656 | 166.38 | -90.75 | 32.99 | |
| -5 | -151.25 | 125 | -75 | 29.99 | |
| -4.5 | -97.5156 | 91.13 | -60.75 | 26.99 | |
| -4 | -59 | 64 | -48 | 23.99 | |
| -3.5 | -32.5156 | 42.88 | -36.75 | 20.99 | |
| -3 | -15.25 | 27 | -27 | 17.99 | |
| -2.5 | -4.7656 | 15.63 | -18.75 | 14.99 | |
| -2.116 | -0.0119 | 9.47 | -13.43 | 12.69 | Nullstelle N(-2.12|-0.01) |
| -2 | 1 | 8 | -12 | 11.99 | |
| -1.5 | 3.7344 | 3.38 | -6.75 | 8.99 | |
| -1 | 4.75 | 1 | -3 | 5.99 | |
| -0.5 | 4.9844 | 0.13 | -0.75 | 2.99 | |
| 0 | 5 | 0 | 0 | -0.01 | Schnittpunkt Sy(0|5) = Hochpunkt H(0|5) |
| 0.5 | 4.9844 | -0.13 | -0.75 | -3.01 | |
| 1 | 4.75 | -1 | -3 | -6.01 | |
| 1.5 | 3.7344 | -3.38 | -6.75 | -9.01 | |
| 2 | 1 | -8 | -12 | -12.01 | |
| 2.114 | 0.007 | -9.45 | -13.41 | -12.69 | Nullstelle N(2.11|0.01) |
| 2.5 | -4.7656 | -15.63 | -18.75 | -15.01 | |
| 3 | -15.25 | -27 | -27 | -18.01 | |
| 3.5 | -32.5156 | -42.88 | -36.75 | -21.01 | |
| 4 | -59 | -64 | -48 | -24.01 | |
| 4.5 | -97.5156 | -91.13 | -60.75 | -27.01 | |
| 5 | -151.25 | -125 | -75 | -30.01 | |
| 5.5 | -223.7656 | -166.38 | -90.75 | -33.01 | |
| 6 | -319 | -216 | -108 | -36.01 | |
| 6.5 | -441.2656 | -274.63 | -126.75 | -39.01 | |
| 7 | -595.25 | -343 | -147 | -42.01 | |
| 7.5 | -786.0156 | -421.88 | -168.75 | -45.01 | |
| 8 | -1019 | -512 | -192 | -48.01 | |
| 8.5 | -1300.0156 | -614.13 | -216.75 | -51.01 | |
| 9 | -1635.25 | -729 | -243 | -54.01 | |
| 9.5 | -2031.2656 | -857.38 | -270.75 | -57.01 | |
| 10 | -2495 | -1000 | -300 | -60.01 | |
| 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