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Funktion: f(x) = (x-5)2/4 + 1, Df = R, Wf = [-8; +∞), allgemeine Parabel (Scheitelform), Funktion achsensymmetrisch zur Senkrechten x = 5, x -> -∞: f(x) -> +∞, x -> +∞: f(x) -> +∞ ->
Wertetabelle: | |||||
x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
-10 | 442 | -60 | 4 | 0 | |
-9.5 | 412.5 | -58 | 4 | 0 | |
-9 | 384 | -56 | 4 | 0 | |
-8.5 | 356.5 | -54 | 4 | 0 | |
-8 | 330 | -52 | 4 | 0 | |
-7.5 | 304.5 | -50 | 4 | 0 | |
-7 | 280 | -48 | 4 | 0 | |
-6.5 | 256.5 | -46 | 4 | 0 | |
-6 | 234 | -44 | 4 | 0 | |
-5.5 | 212.5 | -42 | 4 | 0 | |
-5 | 192 | -40 | 4 | 0 | |
-4.5 | 172.5 | -38 | 4 | 0 | |
-4 | 154 | -36 | 4 | 0 | |
-3.5 | 136.5 | -34 | 4 | 0 | |
-3 | 120 | -32 | 4 | 0 | |
-2.5 | 104.5 | -30 | 4 | 0 | |
-2 | 90 | -28 | 4 | 0 | |
-1.5 | 76.5 | -26 | 4 | 0 | |
-1 | 64 | -24 | 4 | 0 | |
-0.5 | 52.5 | -22 | 4 | 0 | |
0 | 42 | -20 | 4 | 0 | Schnittpunkt Sy(0|42) |
0.5 | 32.5 | -18 | 4 | 0 | |
1 | 24 | -16 | 4 | 0 | |
1.5 | 16.5 | -14 | 4 | 0 | |
2 | 10 | -12 | 4 | 0 | |
2.5 | 4.5 | -10 | 4 | 0 | |
3 | 0 | -8 | 4 | 0 | Nullstelle N(3|0) |
3.5 | -3.5 | -6 | 4 | 0 | |
4 | -6 | -4 | 4 | 0 | |
4.5 | -7.5 | -2 | 4 | 0 | |
5 | -8 | 0 | 4 | 0 | Tiefpunkt T(5|-8) |
5.5 | -7.5 | 2 | 4 | 0 | |
6 | -6 | 4 | 4 | 0 | |
6.5 | -3.5 | 6 | 4 | 0 | |
7 | 0 | 8 | 4 | 0 | Nullstelle N(7|0) |
7.5 | 4.5 | 10 | 4 | 0 | |
8 | 10 | 12 | 4 | 0 | |
8.5 | 16.5 | 14 | 4 | 0 | |
9 | 24 | 16 | 4 | 0 | |
9.5 | 32.5 | 18 | 4 | 0 | |
10 | 42 | 20 | 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