www.michael-buhlmann.de
Funktion: f(x) = (x-2)2/4 + 1, Df = R, Wf = [1; +∞), allgemeine Parabel (Scheitelform), 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 | 37 | -6 | 0.5 | 0 | |
-9.5 | 34.0625 | -5.75 | 0.5 | 0 | |
-9 | 31.25 | -5.5 | 0.5 | 0 | |
-8.5 | 28.5625 | -5.25 | 0.5 | 0 | |
-8 | 26 | -5 | 0.5 | 0 | |
-7.5 | 23.5625 | -4.75 | 0.5 | 0 | |
-7 | 21.25 | -4.5 | 0.5 | 0 | |
-6.5 | 19.0625 | -4.25 | 0.5 | 0 | |
-6 | 17 | -4 | 0.5 | 0 | |
-5.5 | 15.0625 | -3.75 | 0.5 | 0 | |
-5 | 13.25 | -3.5 | 0.5 | 0 | |
-4.5 | 11.5625 | -3.25 | 0.5 | 0 | |
-4 | 10 | -3 | 0.5 | 0 | |
-3.5 | 8.5625 | -2.75 | 0.5 | 0 | |
-3 | 7.25 | -2.5 | 0.5 | 0 | |
-2.5 | 6.0625 | -2.25 | 0.5 | 0 | |
-2 | 5 | -2 | 0.5 | 0 | |
-1.5 | 4.0625 | -1.75 | 0.5 | 0 | |
-1 | 3.25 | -1.5 | 0.5 | 0 | |
-0.5 | 2.5625 | -1.25 | 0.5 | 0 | |
0 | 2 | -1 | 0.5 | 0 | Schnittpunkt Sy(0|2) |
0.5 | 1.5625 | -0.75 | 0.5 | 0 | |
1 | 1.25 | -0.5 | 0.5 | 0 | |
1.5 | 1.0625 | -0.25 | 0.5 | 0 | |
2 | 1 | 0 | 0.5 | 0 | Tiefpunkt T(2|1) |
2.5 | 1.0625 | 0.25 | 0.5 | 0 | |
3 | 1.25 | 0.5 | 0.5 | 0 | |
3.5 | 1.5625 | 0.75 | 0.5 | 0 | |
4 | 2 | 1 | 0.5 | 0 | |
4.5 | 2.5625 | 1.25 | 0.5 | 0 | |
5 | 3.25 | 1.5 | 0.5 | 0 | |
5.5 | 4.0625 | 1.75 | 0.5 | 0 | |
6 | 5 | 2 | 0.5 | 0 | |
6.5 | 6.0625 | 2.25 | 0.5 | 0 | |
7 | 7.25 | 2.5 | 0.5 | 0 | |
7.5 | 8.5625 | 2.75 | 0.5 | 0 | |
8 | 10 | 3 | 0.5 | 0 | |
8.5 | 11.5625 | 3.25 | 0.5 | 0 | |
9 | 13.25 | 3.5 | 0.5 | 0 | |
9.5 | 15.0625 | 3.75 | 0.5 | 0 | |
10 | 17 | 4 | 0.5 | 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