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Funktion: f(x) = -x4 + 29x2 - 100, Df = R, Wf = (-∞; 110.25], Polynom 4. Grades, 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 | -7200 | 3420 | -1142 | 239.99 | |
| -9.5 | -5627.8125 | 2878.5 | -1025 | 227.99 | |
| -9 | -4312 | 2394 | -914 | 215.99 | |
| -8.5 | -3224.8125 | 1963.5 | -809 | 203.99 | |
| -8 | -2340 | 1584 | -710 | 191.99 | |
| -7.5 | -1632.8125 | 1252.5 | -617 | 179.99 | |
| -7 | -1080 | 966 | -530 | 167.99 | |
| -6.5 | -659.8125 | 721.5 | -449 | 155.99 | |
| -6 | -352 | 516 | -374 | 143.99 | |
| -5.5 | -137.8125 | 346.5 | -305 | 131.99 | |
| -5 | 0 | 210 | -242 | 119.99 | Nullstelle N(-5|0) |
| -4.5 | 77.1875 | 103.5 | -185 | 107.99 | |
| -4 | 108 | 24 | -134 | 95.99 | |
| -3.808 | 110.25 | 0 | -116.01 | 91.38 | Hochpunkt H(-3.81|110.25) |
| -3.5 | 105.1875 | -31.5 | -89 | 83.99 | |
| -3 | 80 | -66 | -50 | 71.99 | |
| -2.5 | 42.1875 | -82.5 | -17 | 59.99 | |
| -2.2 | 16.8 | -85.01 | 0 | 52.76 | Wendepunkt W(-2.2|16.8) |
| -2 | 0 | -84 | 10 | 47.99 | Nullstelle N(-2|0) |
| -1.5 | -39.8125 | -73.5 | 31 | 35.99 | |
| -1 | -72 | -54 | 46 | 23.99 | |
| -0.5 | -92.8125 | -28.5 | 55 | 11.99 | |
| 0 | -100 | 0 | 58 | -0.01 | Schnittpunkt Sy(0|-100) = Tiefpunkt T(0|-100) |
| 0.5 | -92.8125 | 28.5 | 55 | -12.01 | |
| 1 | -72 | 54 | 46 | -24.01 | |
| 1.5 | -39.8125 | 73.5 | 31 | -36.01 | |
| 2 | 0 | 84 | 10 | -48.01 | Nullstelle N(2|0) |
| 2.2 | 16.8 | 85.01 | 0.03 | -52.76 | Wendepunkt W(2.2|16.8) |
| 2.5 | 42.1875 | 82.5 | -17 | -60.01 | |
| 3 | 80 | 66 | -50 | -72.01 | |
| 3.5 | 105.1875 | 31.5 | -89 | -84.01 | |
| 3.807 | 110.25 | 0 | -115.92 | -91.38 | Hochpunkt H(3.81|110.25) |
| 4 | 108 | -24 | -134 | -96.01 | |
| 4.5 | 77.1875 | -103.5 | -185 | -108.01 | |
| 5 | 0 | -210 | -242 | -120.01 | Nullstelle N(5|0) |
| 5.5 | -137.8125 | -346.5 | -305 | -132.01 | |
| 6 | -352 | -516 | -374 | -144.01 | |
| 6.5 | -659.8125 | -721.5 | -449 | -156.01 | |
| 7 | -1080 | -966 | -530 | -168.01 | |
| 7.5 | -1632.8125 | -1252.5 | -617 | -180.01 | |
| 8 | -2340 | -1584 | -710 | -192.02 | |
| 8.5 | -3224.8125 | -1963.5 | -809 | -204.01 | |
| 9 | -4312 | -2394 | -914 | -216.01 | |
| 9.5 | -5627.8125 | -2878.5 | -1025 | -228.02 | |
| 10 | -7200 | -3420 | -1142 | -240.02 | |
| 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