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Funktion: f(x) = -x3/8 + x2/2 + 5x, Df = R, Wf = R, Polynom 3. Grades, Funktion punktsymmetrisch zum Punkt W(1.33|7.26), x -> -∞: f(x) -> +∞, x -> +∞: f(x) -> -∞ ->
Wertetabelle: | |||||
x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
-10 | 125 | -42.5 | 8.5 | -0.75 | |
-9.5 | 104.7969 | -38.34 | 8.12 | -0.75 | |
-9 | 86.625 | -34.38 | 7.75 | -0.75 | |
-8.5 | 70.3906 | -30.59 | 7.37 | -0.75 | |
-8 | 56 | -27 | 7 | -0.75 | |
-7.5 | 43.3594 | -23.59 | 6.63 | -0.75 | |
-7 | 32.375 | -20.38 | 6.25 | -0.75 | |
-6.5 | 22.9531 | -17.34 | 5.88 | -0.75 | |
-6 | 15 | -14.5 | 5.5 | -0.75 | |
-5.5 | 8.4219 | -11.84 | 5.13 | -0.75 | |
-5 | 3.125 | -9.38 | 4.75 | -0.75 | |
-4.634 | 0 | -7.69 | 4.48 | -0.75 | Nullstelle N(-4.63|0) |
-4.5 | -0.9844 | -7.09 | 4.37 | -0.75 | |
-4 | -4 | -5 | 4 | -0.75 | |
-3.5 | -6.0156 | -3.09 | 3.62 | -0.75 | |
-3 | -7.125 | -1.38 | 3.25 | -0.75 | |
-2.554 | -7.4261 | 0 | 2.92 | -0.75 | Tiefpunkt T(-2.55|-7.43) |
-2.5 | -7.4219 | 0.16 | 2.87 | -0.75 | |
-2 | -7 | 1.5 | 2.5 | -0.75 | |
-1.5 | -5.9531 | 2.66 | 2.12 | -0.75 | |
-1 | -4.375 | 3.62 | 1.75 | -0.75 | |
-0.5 | -2.3594 | 4.41 | 1.38 | -0.75 | |
0 | 0 | 5 | 1 | -0.75 | Nullstelle N(0|0) = Schnittpunkt Sy(0|0) |
0.5 | 2.6094 | 5.41 | 0.63 | -0.75 | |
1 | 5.375 | 5.62 | 0.25 | -0.75 | |
1.333 | 7.2574 | 5.67 | 0 | -0.75 | Wendepunkt W(1.33|7.26) |
1.5 | 8.2031 | 5.66 | -0.12 | -0.75 | |
2 | 11 | 5.5 | -0.5 | -0.75 | |
2.5 | 13.6719 | 5.16 | -0.87 | -0.75 | |
3 | 16.125 | 4.62 | -1.25 | -0.75 | |
3.5 | 18.2656 | 3.91 | -1.62 | -0.75 | |
4 | 20 | 3 | -2 | -0.75 | |
4.5 | 21.2344 | 1.91 | -2.38 | -0.75 | |
5 | 21.875 | 0.62 | -2.75 | -0.75 | |
5.22 | 21.9446 | 0 | -2.91 | -0.75 | Hochpunkt H(5.22|21.94) |
5.5 | 21.8281 | -0.84 | -3.12 | -0.75 | |
6 | 21 | -2.5 | -3.5 | -0.75 | |
6.5 | 19.2969 | -4.34 | -3.87 | -0.75 | |
7 | 16.625 | -6.38 | -4.25 | -0.75 | |
7.5 | 12.8906 | -8.59 | -4.63 | -0.75 | |
8 | 8 | -11 | -5 | -0.75 | |
8.5 | 1.8594 | -13.59 | -5.38 | -0.75 | |
8.633 | 0 | -14.32 | -5.47 | -0.75 | Nullstelle N(8.63|0) |
9 | -5.625 | -16.38 | -5.75 | -0.75 | |
9.5 | -14.5469 | -19.34 | -6.12 | -0.75 | |
10 | -25 | -22.5 | -6.5 | -0.75 | |
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