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Funktion: f(x) = x2(x+4)2/4, Df = R, Wf = [0; +∞), Polynom 4. Grades, Funktion achsensymmetrisch zur Senkrechten x = -2, x -> -∞: f(x) -> +∞, x -> +∞: f(x) -> +∞ ->
| Wertetabelle: | |||||
| x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
| -10 | 900 | -480 | 188 | -48 | |
| -9.5 | 682.5156 | -391.88 | 164.75 | -45 | |
| -9 | 506.25 | -315 | 143 | -42 | |
| -8.5 | 365.7656 | -248.63 | 122.75 | -39 | |
| -8 | 256 | -192 | 104 | -36 | |
| -7.5 | 172.2656 | -144.38 | 86.75 | -33 | |
| -7 | 110.25 | -105 | 71 | -30 | |
| -6.5 | 66.0156 | -73.13 | 56.75 | -27 | |
| -6 | 36 | -48 | 44 | -24 | |
| -5.5 | 17.0156 | -28.88 | 32.75 | -21 | |
| -5 | 6.25 | -15 | 23 | -18 | |
| -4.5 | 1.2656 | -5.63 | 14.75 | -15 | |
| -4 | 0 | 0 | 8 | -12 | Nullstelle N(-4|0) = Tiefpunkt T(-4|0) |
| -3.5 | 0.7656 | 2.62 | 2.75 | -9 | |
| -3.155 | 1.7769 | 3.08 | 0 | -6.93 | Wendepunkt W(-3.15|1.78) |
| -3 | 2.25 | 3 | -1 | -6 | |
| -2.5 | 3.5156 | 1.87 | -3.25 | -3 | |
| -2 | 4 | 0 | -4 | 0 | Hochpunkt H(-2|4) |
| -1.5 | 3.5156 | -1.87 | -3.25 | 3 | |
| -1 | 2.25 | -3 | -1 | 6 | |
| -0.846 | 1.7799 | -3.08 | 0 | 6.93 | Wendepunkt W(-0.85|1.78) |
| -0.5 | 0.7656 | -2.62 | 2.75 | 9 | |
| 0 | 0 | 0 | 8 | 12 | Nullstelle N(0|0) = Schnittpunkt Sy(0|0) = Tiefpunkt T(0|0) |
| 0.5 | 1.2656 | 5.63 | 14.75 | 15 | |
| 1 | 6.25 | 15 | 23 | 18 | |
| 1.5 | 17.0156 | 28.88 | 32.75 | 21 | |
| 2 | 36 | 48 | 44 | 24 | |
| 2.5 | 66.0156 | 73.13 | 56.75 | 27 | |
| 3 | 110.25 | 105 | 71 | 30 | |
| 3.5 | 172.2656 | 144.38 | 86.75 | 33 | |
| 4 | 256 | 192 | 104 | 36 | |
| 4.5 | 365.7656 | 248.63 | 122.75 | 39 | |
| 5 | 506.25 | 315 | 143 | 42 | |
| 5.5 | 682.5156 | 391.88 | 164.75 | 45 | |
| 6 | 900 | 480 | 188 | 48 | |
| 6.5 | 1164.5156 | 580.13 | 212.75 | 51 | |
| 7 | 1482.25 | 693 | 239 | 54 | |
| 7.5 | 1859.7656 | 819.38 | 266.75 | 57 | |
| 8 | 2304 | 960 | 296 | 60.01 | |
| 8.5 | 2822.2656 | 1115.63 | 326.75 | 63 | |
| 9 | 3422.25 | 1287 | 359 | 66 | |
| 9.5 | 4112.0156 | 1474.88 | 392.75 | 69.01 | |
| 10 | 4900 | 1680 | 428 | 72.01 | |
| 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