www.michael-buhlmann.de
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: | |||||
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