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Funktion: f(x) = -x(2x-19/2), Df = R, Wf = (-∞; 11.28125], allgemeine Parabel (2. Grades; Produktform), Funktion achsensymmetrisch zur Senkrechten x = 19/8, x -> -∞: f(x) -> -∞, x -> +∞: f(x) -> -∞ ->
| Wertetabelle: | |||||
| x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
| -15 | -592.5 | 69.5 | -4 | 0 | |
| -14.5 | -558.25 | 67.5 | -4 | 0 | |
| -14 | -525 | 65.5 | -4 | 0 | |
| -13.5 | -492.75 | 63.5 | -4 | 0 | |
| -13 | -461.5 | 61.5 | -4 | 0 | |
| -12.5 | -431.25 | 59.5 | -4 | 0 | |
| -12 | -402 | 57.5 | -4 | 0 | |
| -11.5 | -373.75 | 55.5 | -4 | 0 | |
| -11 | -346.5 | 53.5 | -4 | 0 | |
| -10.5 | -320.25 | 51.5 | -4 | 0 | |
| -10 | -295 | 49.5 | -4 | 0 | |
| -9.5 | -270.75 | 47.5 | -4 | 0 | |
| -9 | -247.5 | 45.5 | -4 | 0 | |
| -8.5 | -225.25 | 43.5 | -4 | 0 | |
| -8 | -204 | 41.5 | -4 | 0 | |
| -7.5 | -183.75 | 39.5 | -4 | 0 | |
| -7 | -164.5 | 37.5 | -4 | 0 | |
| -6.5 | -146.25 | 35.5 | -4 | 0 | |
| -6 | -129 | 33.5 | -4 | 0 | |
| -5.5 | -112.75 | 31.5 | -4 | 0 | |
| -5 | -97.5 | 29.5 | -4 | 0 | |
| -4.5 | -83.25 | 27.5 | -4 | 0 | |
| -4 | -70 | 25.5 | -4 | 0 | |
| -3.5 | -57.75 | 23.5 | -4 | 0 | |
| -3 | -46.5 | 21.5 | -4 | 0 | |
| -2.5 | -36.25 | 19.5 | -4 | 0 | |
| -2 | -27 | 17.5 | -4 | 0 | |
| -1.5 | -18.75 | 15.5 | -4 | 0 | |
| -1 | -11.5 | 13.5 | -4 | 0 | |
| -0.5 | -5.25 | 11.5 | -4 | 0 | |
| 0 | 0 | 9.5 | -4 | 0 | Nullstelle N(0|0) = Schnittpunkt Sy(0|0) |
| 0.5 | 4.25 | 7.5 | -4 | 0 | |
| 1 | 7.5 | 5.5 | -4 | 0 | |
| 1.5 | 9.75 | 3.5 | -4 | 0 | |
| 2 | 11 | 1.5 | -4 | 0 | |
| 2.375 | 11.28125 | 0.02 | -4 | 0 | Hochpunkt H(2.375|11.28125) |
| 2.5 | 11.25 | -0.5 | -4 | 0 | |
| 3 | 10.5 | -2.5 | -4 | 0 | |
| 3.5 | 8.75 | -4.5 | -4 | 0 | |
| 4 | 6 | -6.5 | -4 | 0 | |
| 4.5 | 2.25 | -8.5 | -4 | 0 | |
| 4.75 | 0 | -9.5 | -4 | 0 | Nullstelle N(4.75|0) |
| 5 | -2.5 | -10.5 | -4 | 0 | |
| 5.5 | -8.25 | -12.5 | -4 | 0 | |
| 6 | -15 | -14.5 | -4 | 0 | |
| 6.5 | -22.75 | -16.5 | -4 | 0 | |
| 7 | -31.5 | -18.5 | -4 | 0 | |
| 7.5 | -41.25 | -20.5 | -4 | 0 | |
| 8 | -52 | -22.5 | -4 | 0 | |
| 8.5 | -63.75 | -24.5 | -4 | 0 | |
| 9 | -76.5 | -26.5 | -4 | 0 | |
| 9.5 | -90.25 | -28.5 | -4 | 0 | |
| 10 | -105 | -30.5 | -4 | 0 | |
| 10.5 | -120.75 | -32.5 | -4 | 0 | |
| 11 | -137.5 | -34.5 | -4 | 0 | |
| 11.5 | -155.25 | -36.5 | -4 | 0 | |
| 12 | -174 | -38.5 | -4 | 0 | |
| 12.5 | -193.75 | -40.5 | -4 | 0 | |
| 13 | -214.5 | -42.5 | -4 | 0 | |
| 13.5 | -236.25 | -44.5 | -4 | 0 | |
| 14 | -259 | -46.5 | -4 | 0 | |
| 14.5 | -282.75 | -48.5 | -4 | 0 | |
| 15 | -307.5 | -50.5 | -4 | 0 | |
| 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