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Funktion: f(x) = -x3 + 3x2 - 3x + 11, Df = R, Wf = R, Polynom 3. Grades, Funktion punktsymmetrisch zum Punkt W(1|10), x -> -∞: f(x) -> +∞, x -> +∞: f(x) -> -∞ ->
Wertetabelle: | |||||
x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
-10 | 1341 | -363 | 66 | -6 | |
-9.5 | 1167.625 | -330.75 | 63 | -6 | |
-9 | 1010 | -300 | 60 | -6 | |
-8.5 | 867.375 | -270.75 | 57 | -6 | |
-8 | 739 | -243 | 54 | -6 | |
-7.5 | 624.125 | -216.75 | 51 | -6 | |
-7 | 522 | -192 | 48 | -6 | |
-6.5 | 431.875 | -168.75 | 45 | -6 | |
-6 | 353 | -147 | 42 | -6 | |
-5.5 | 284.625 | -126.75 | 39 | -6 | |
-5 | 226 | -108 | 36 | -6 | |
-4.5 | 176.375 | -90.75 | 33 | -6 | |
-4 | 135 | -75 | 30 | -6 | |
-3.5 | 101.125 | -60.75 | 27 | -6 | |
-3 | 74 | -48 | 24 | -6 | |
-2.5 | 52.875 | -36.75 | 21 | -6 | |
-2 | 37 | -27 | 18 | -6 | |
-1.5 | 25.625 | -18.75 | 15 | -6 | |
-1 | 18 | -12 | 12 | -6 | |
-0.5 | 13.375 | -6.75 | 9 | -6 | |
0 | 11 | -3 | 6 | -6 | Schnittpunkt Sy(0|11) |
0.5 | 10.125 | -0.75 | 3 | -6 | |
1 | 10 | 0 | 0 | -6 | Wendepunkt W(1|10) = Sattelpunkt WS(1|10) |
1.5 | 9.875 | -0.75 | -3 | -6 | |
2 | 9 | -3 | -6 | -6 | |
2.5 | 6.625 | -6.75 | -9 | -6 | |
3 | 2 | -12 | -12 | -6 | |
3.154 | 0 | -13.92 | -12.92 | -6 | Nullstelle N(3.15|0) |
3.5 | -5.625 | -18.75 | -15 | -6 | |
4 | -17 | -27 | -18 | -6 | |
4.5 | -32.875 | -36.75 | -21 | -6 | |
5 | -54 | -48 | -24 | -6 | |
5.5 | -81.125 | -60.75 | -27 | -6 | |
6 | -115 | -75 | -30 | -6 | |
6.5 | -156.375 | -90.75 | -33 | -6 | |
7 | -206 | -108 | -36 | -6 | |
7.5 | -264.625 | -126.75 | -39 | -6 | |
8 | -333 | -147 | -42 | -6 | |
8.5 | -411.875 | -168.75 | -45 | -6 | |
9 | -502 | -192 | -48 | -6 | |
9.5 | -604.125 | -216.75 | -51 | -6 | |
10 | -719 | -243 | -54 | -6 | |
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