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Funktion: f(x) = x4 + 2x2 - 12x + 5, Df = R, Wf = [-4.4482; +∞), Polynom 4. Grades, x -> -∞: f(x) -> +∞, x -> +∞: f(x) -> +∞ ->
| Wertetabelle: | |||||
| x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
| -5 | 740 | -532 | 304 | -119.88 | |
| -4.5 | 509.5625 | -394.5 | 247 | -107.88 | |
| -4 | 341 | -284 | 196 | -95.88 | |
| -3.5 | 221.5625 | -197.5 | 151 | -83.88 | |
| -3 | 140 | -132 | 112 | -71.88 | |
| -2.5 | 86.5625 | -84.5 | 79 | -59.88 | |
| -2 | 53 | -52 | 52 | -47.88 | |
| -1.5 | 32.5625 | -31.5 | 31 | -35.88 | |
| -1 | 20 | -20 | 16 | -23.88 | |
| -0.5 | 11.5625 | -14.5 | 7 | -11.88 | |
| 0 | 5 | -12 | 4 | 0.12 | Schnittpunkt Sy(0|5) |
| 0.45 | 0 | -9.84 | 6.43 | 10.92 | Nullstelle N(0.45|0) |
| 0.5 | -0.4375 | -9.5 | 7 | 12.12 | |
| 1 | -4 | -4 | 16 | 24.12 | |
| 1.21 | -4.4482 | 0 | 21.57 | 29.16 | Tiefpunkt T(1.21|-4.45) |
| 1.5 | -3.4375 | 7.5 | 31 | 36.12 | |
| 1.77 | 0 | 17.26 | 41.6 | 42.6 | Nullstelle N(1.77|0.16) |
| 2 | 5 | 28 | 52 | 48.12 | |
| 2.5 | 26.5625 | 60.5 | 79 | 60.12 | |
| 3 | 68 | 108 | 112 | 72.12 | |
| 3.5 | 137.5625 | 173.5 | 151 | 84.12 | |
| 4 | 245 | 260 | 196 | 96.12 | |
| 4.5 | 401.5625 | 370.5 | 247 | 108.12 | |
| 5 | 620 | 508 | 304 | 120.12 | |
| 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