www.michael-buhlmann.de
Funktion: f(x) = 3x2 + 9x - 12, Df = R, Wf = [-18.75; +∞), allgemeine Parabel (Normalform; Scheitelform: f(x) = 3(x+1.5)2 - 18.75), Funktion achsensymmetrisch zur Senkrechten x = -1.5, x -> -∞: f(x) -> +∞, x -> +∞: f(x) -> +∞ ->
Wertetabelle: | |||||
x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
-10 | 198 | -51 | 6 | 0 | |
-9.5 | 173.25 | -48 | 6 | 0 | |
-9 | 150 | -45 | 6 | 0 | |
-8.5 | 128.25 | -42 | 6 | 0 | |
-8 | 108 | -39 | 6 | 0 | |
-7.5 | 89.25 | -36 | 6 | 0 | |
-7 | 72 | -33 | 6 | 0 | |
-6.5 | 56.25 | -30 | 6 | 0 | |
-6 | 42 | -27 | 6 | 0 | |
-5.5 | 29.25 | -24 | 6 | 0 | |
-5 | 18 | -21 | 6 | 0 | |
-4.5 | 8.25 | -18 | 6 | 0 | |
-4 | 0 | -15 | 6 | 0 | Nullstelle N(-4|0) |
-3.5 | -6.75 | -12 | 6 | 0 | |
-3 | -12 | -9 | 6 | 0 | |
-2.5 | -15.75 | -6 | 6 | 0 | |
-2 | -18 | -3 | 6 | 0 | |
-1.5 | -18.75 | 0 | 6 | 0 | Tiefpunkt T(-1.5|-18.75) |
-1 | -18 | 3 | 6 | 0 | |
-0.5 | -15.75 | 6 | 6 | 0 | |
0 | -12 | 9 | 6 | 0 | Schnittpunkt Sy(0|-12) |
0.5 | -6.75 | 12 | 6 | 0 | |
1 | 0 | 15 | 6 | 0 | Nullstelle N(1|0) |
1.5 | 8.25 | 18 | 6 | 0 | |
2 | 18 | 21 | 6 | 0 | |
2.5 | 29.25 | 24 | 6 | 0 | |
3 | 42 | 27 | 6 | 0 | |
3.5 | 56.25 | 30 | 6 | 0 | |
4 | 72 | 33 | 6 | 0 | |
4.5 | 89.25 | 36 | 6 | 0 | |
5 | 108 | 39 | 6 | 0 | |
5.5 | 128.25 | 42 | 6 | 0 | |
6 | 150 | 45 | 6 | 0 | |
6.5 | 173.25 | 48 | 6 | 0 | |
7 | 198 | 51 | 6 | 0 | |
7.5 | 224.25 | 54 | 6 | 0 | |
8 | 252 | 57 | 6 | 0 | |
8.5 | 281.25 | 60 | 6 | 0 | |
9 | 312 | 63 | 6 | 0 | |
9.5 | 344.25 | 66 | 6 | 0 | |
10 | 378 | 69 | 6 | 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