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Funktion: f(x) = -x2/5 - x, Df = R, Wf = (-∞; 1.25], allgemeine Parabel (Normalform; Scheitelform: f(x) = -0.2·(x+2.5)2 + 1.25), Funktion achsensymmetrisch zur Senkrechten x = -2.5, x -> -∞: f(x) -> -∞, x -> +∞: f(x) -> -∞ ->
Wertetabelle: | |||||
x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
-10 | -10 | 3 | -0.4 | 0 | |
-9.5 | -8.55 | 2.8 | -0.4 | 0 | |
-9 | -7.2 | 2.6 | -0.4 | 0 | |
-8.5 | -5.95 | 2.4 | -0.4 | 0 | |
-8 | -4.8 | 2.2 | -0.4 | 0 | |
-7.5 | -3.75 | 2 | -0.4 | 0 | |
-7 | -2.8 | 1.8 | -0.4 | 0 | |
-6.5 | -1.95 | 1.6 | -0.4 | 0 | |
-6 | -1.2 | 1.4 | -0.4 | 0 | |
-5.5 | -0.55 | 1.2 | -0.4 | 0 | |
-5 | 0 | 1 | -0.4 | 0 | Nullstelle N(-5|0) |
-4.5 | 0.45 | 0.8 | -0.4 | 0 | |
-4 | 0.8 | 0.6 | -0.4 | 0 | |
-3.5 | 1.05 | 0.4 | -0.4 | 0 | |
-3 | 1.2 | 0.2 | -0.4 | 0 | |
-2.5 | 1.25 | 0 | -0.4 | 0 | Hochpunkt H(-2.5|1.25) |
-2 | 1.2 | -0.2 | -0.4 | 0 | |
-1.5 | 1.05 | -0.4 | -0.4 | 0 | |
-1 | 0.8 | -0.6 | -0.4 | 0 | |
-0.5 | 0.45 | -0.8 | -0.4 | 0 | |
0 | 0 | -1 | -0.4 | 0 | Nullstelle N(0|0) = Schnittpunkt Sy(0|0) |
0.5 | -0.55 | -1.2 | -0.4 | 0 | |
1 | -1.2 | -1.4 | -0.4 | 0 | |
1.5 | -1.95 | -1.6 | -0.4 | 0 | |
2 | -2.8 | -1.8 | -0.4 | 0 | |
2.5 | -3.75 | -2 | -0.4 | 0 | |
3 | -4.8 | -2.2 | -0.4 | 0 | |
3.5 | -5.95 | -2.4 | -0.4 | 0 | |
4 | -7.2 | -2.6 | -0.4 | 0 | |
4.5 | -8.55 | -2.8 | -0.4 | 0 | |
5 | -10 | -3 | -0.4 | 0 | |
5.5 | -11.55 | -3.2 | -0.4 | 0 | |
6 | -13.2 | -3.4 | -0.4 | 0 | |
6.5 | -14.95 | -3.6 | -0.4 | 0 | |
7 | -16.8 | -3.8 | -0.4 | 0 | |
7.5 | -18.75 | -4 | -0.4 | 0 | |
8 | -20.8 | -4.2 | -0.4 | 0 | |
8.5 | -22.95 | -4.4 | -0.4 | 0 | |
9 | -25.2 | -4.6 | -0.4 | 0 | |
9.5 | -27.55 | -4.8 | -0.4 | 0 | |
10 | -30 | -5 | -0.4 | 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