www.michael-buhlmann.de
Funktion: f(x) = 2x3 + 5x - 7, Df = R, Wf = R, Polynom 3. Grades, Funktion punktsymmetrisch zum Punkt W(0|-7), x -> -∞: f(x) -> -∞, x -> +∞: f(x) -> +∞ ->
Wertetabelle: | |||||
x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
-10 | -2057 | 605 | -120 | 12 | |
-9.5 | -1769.25 | 546.5 | -114 | 12 | |
-9 | -1510 | 491 | -108 | 12 | |
-8.5 | -1277.75 | 438.5 | -102 | 12 | |
-8 | -1071 | 389 | -96 | 12 | |
-7.5 | -888.25 | 342.5 | -90 | 12 | |
-7 | -728 | 299 | -84 | 12 | |
-6.5 | -588.75 | 258.5 | -78 | 12 | |
-6 | -469 | 221 | -72 | 12 | |
-5.5 | -367.25 | 186.5 | -66 | 12 | |
-5 | -282 | 155 | -60 | 12 | |
-4.5 | -211.75 | 126.5 | -54 | 12 | |
-4 | -155 | 101 | -48 | 12 | |
-3.5 | -110.25 | 78.5 | -42 | 12 | |
-3 | -76 | 59 | -36 | 12 | |
-2.5 | -50.75 | 42.5 | -30 | 12 | |
-2 | -33 | 29 | -24 | 12 | |
-1.5 | -21.25 | 18.5 | -18 | 12 | |
-1 | -14 | 11 | -12 | 12 | |
-0.5 | -9.75 | 6.5 | -6 | 12 | |
0 | -7 | 5 | 0 | 12 | Schnittpunkt Sy(0|-7) = Wendepunkt W(0|-7) |
0.5 | -4.25 | 6.5 | 6 | 12 | |
1 | 0 | 11 | 12 | 12 | Nullstelle N(1|0) |
1.5 | 7.25 | 18.5 | 18 | 12 | |
2 | 19 | 29 | 24 | 12 | |
2.5 | 36.75 | 42.5 | 30 | 12 | |
3 | 62 | 59 | 36 | 12 | |
3.5 | 96.25 | 78.5 | 42 | 12 | |
4 | 141 | 101 | 48 | 12 | |
4.5 | 197.75 | 126.5 | 54 | 12 | |
5 | 268 | 155 | 60 | 12 | |
5.5 | 353.25 | 186.5 | 66 | 12 | |
6 | 455 | 221 | 72 | 12 | |
6.5 | 574.75 | 258.5 | 78 | 12 | |
7 | 714 | 299 | 84 | 12 | |
7.5 | 874.25 | 342.5 | 90 | 12 | |
8 | 1057 | 389 | 96 | 12 | |
8.5 | 1263.75 | 438.5 | 102 | 12 | |
9 | 1496 | 491 | 108 | 12 | |
9.5 | 1755.25 | 546.5 | 114 | 12 | |
10 | 2043 | 605 | 120 | 12 | |
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