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Funktion: f(x) = -1.5·x2, Df = R, Wf = (-∞; 0], allgemeine Parabel als gestreckte Normalparabel, um die x-Achse gespiegelt, Funktion achsensymmetrisch zur Senkrechten x = 0, x -> -∞: f(x) -> -∞, x -> +∞: f(x) -> -∞ ->
Wertetabelle: | |||||
x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
-10 | -150 | 30 | -3 | 0 | |
-9.5 | -135.375 | 28.5 | -3 | 0 | |
-9 | -121.5 | 27 | -3 | 0 | |
-8.5 | -108.375 | 25.5 | -3 | 0 | |
-8 | -96 | 24 | -3 | 0 | |
-7.5 | -84.375 | 22.5 | -3 | 0 | |
-7 | -73.5 | 21 | -3 | 0 | |
-6.5 | -63.375 | 19.5 | -3 | 0 | |
-6 | -54 | 18 | -3 | 0 | |
-5.5 | -45.375 | 16.5 | -3 | 0 | |
-5 | -37.5 | 15 | -3 | 0 | |
-4.5 | -30.375 | 13.5 | -3 | 0 | |
-4 | -24 | 12 | -3 | 0 | |
-3.5 | -18.375 | 10.5 | -3 | 0 | |
-3 | -13.5 | 9 | -3 | 0 | |
-2.5 | -9.375 | 7.5 | -3 | 0 | |
-2 | -6 | 6 | -3 | 0 | |
-1.5 | -3.375 | 4.5 | -3 | 0 | |
-1 | -1.5 | 3 | -3 | 0 | |
-0.5 | -0.375 | 1.5 | -3 | 0 | |
0 | 0 | 0 | -3 | 0 | Nullstelle N(0|0) = Schnittpunkt Sy(0|0) = Hochpunkt H(0|0) |
0.5 | -0.375 | -1.5 | -3 | 0 | |
1 | -1.5 | -3 | -3 | 0 | |
1.5 | -3.375 | -4.5 | -3 | 0 | |
2 | -6 | -6 | -3 | 0 | |
2.5 | -9.375 | -7.5 | -3 | 0 | |
3 | -13.5 | -9 | -3 | 0 | |
3.5 | -18.375 | -10.5 | -3 | 0 | |
4 | -24 | -12 | -3 | 0 | |
4.5 | -30.375 | -13.5 | -3 | 0 | |
5 | -37.5 | -15 | -3 | 0 | |
5.5 | -45.375 | -16.5 | -3 | 0 | |
6 | -54 | -18 | -3 | 0 | |
6.5 | -63.375 | -19.5 | -3 | 0 | |
7 | -73.5 | -21 | -3 | 0 | |
7.5 | -84.375 | -22.5 | -3 | 0 | |
8 | -96 | -24 | -3 | 0 | |
8.5 | -108.375 | -25.5 | -3 | 0 | |
9 | -121.5 | -27 | -3 | 0 | |
9.5 | -135.375 | -28.5 | -3 | 0 | |
10 | -150 | -30 | -3 | 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