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Funktion: f(x) = x3·sin(2x)/80, Df = R, Wf = R, reelle Funktion, Funktion achsensymmetrisch zur Senkrechten x = 0 ->
| Wertetabelle: | |||||
| x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
| -10 | 11.4118 | -13.63 | -38.84 | 80.1 | |
| -9.58 | 3.3573 | -21.98 | -0.1 | 92.15 | Wendepunkt W(-9.58|3.36) |
| -9.5 | 1.6063 | -21.7 | 7.07 | 86.53 | |
| -9.426 | 0.0256 | -20.95 | 13.23 | 79.5 | Nullstelle N(-9.43|0.03) |
| -9 | -6.8434 | -9.75 | 34.89 | 17.98 | |
| -8.726 | -8.181 | -0.05 | 34.05 | -23.03 | Tiefpunkt T(-8.73|-8.18) |
| -8.5 | -7.3802 | 6.83 | 25.93 | -47.11 | |
| -8.038 | -2.3356 | 12.99 | 0.08 | -55.47 | Wendepunkt W(-8.04|-2.34) |
| -8 | -1.8426 | 12.95 | -2 | -53.81 | |
| -7.854 | -0.0002 | 12.11 | -9.25 | -44.84 | Nullstelle N(-7.85|0) |
| -7.5 | 3.4293 | 6.64 | -19.76 | -12.98 | |
| -7.172 | 4.5131 | 0.01 | -19.11 | 15.74 | Hochpunkt H(-7.17|4.51) |
| -7 | 4.2472 | -2.99 | -15.46 | 26.08 | |
| -6.508 | 1.4975 | -6.9 | -0.06 | 30.41 | Wendepunkt W(-6.51|1.5) |
| -6.5 | 1.4424 | -6.9 | 0.19 | 30.2 | |
| -6.284 | 0.0051 | -6.21 | 5.9 | 21.97 | Nullstelle N(-6.28|0.01) |
| -6 | -1.4487 | -3.83 | 10.11 | 7.24 | |
| -5.63 | -2.1531 | -0.02 | 9.45 | -9.73 | Tiefpunkt T(-5.63|-2.15) |
| -5.5 | -2.0797 | 1.12 | 7.93 | -13.5 | |
| -5 | -0.85 | 3.13 | 0.05 | -14.66 | |
| -4.998 | -0.8438 | 3.13 | 0.02 | -14.63 | Wendepunkt W(-5|-0.84) |
| -4.714 | -0.0042 | 2.62 | -3.32 | -8.36 | Nullstelle N(-4.71|0) |
| -4.5 | 0.4694 | 1.76 | -4.51 | -2.71 | |
| -4.104 | 0.8105 | 0.01 | -3.83 | 5.3 | Hochpunkt H(-4.1|0.81) |
| -4 | 0.7915 | -0.36 | -3.22 | 6.39 | |
| -3.528 | 0.3832 | -1.11 | -0.01 | 5.86 | Wendepunkt W(-3.53|0.38) |
| -3.5 | 0.3521 | -1.11 | 0.15 | 5.61 | |
| -3.142 | 0.0003 | -0.78 | 1.48 | 1.68 | Nullstelle N(-3.14|0) |
| -3 | -0.0943 | -0.55 | 1.61 | 0.18 | |
| -2.618 | -0.1942 | 0 | 1.12 | -2.3 | Tiefpunkt T(-2.62|-0.19) |
| -2.5 | -0.1873 | 0.11 | 0.84 | -2.5 | |
| -2.134 | -0.1097 | 0.26 | 0 | -1.78 | Wendepunkt W(-2.13|-0.11) |
| -2 | -0.0757 | 0.24 | -0.2 | -1.24 | |
| -1.572 | -0.0001 | 0.1 | -0.37 | 0.32 | Nullstelle N(-1.57|0) |
| -1.5 | 0.006 | 0.07 | -0.34 | 0.47 | |
| -1.228 | 0.0147 | 0 | -0.18 | 0.67 | Hochpunkt H(-1.23|0.01) |
| -1 | 0.0114 | -0.02 | -0.04 | 0.49 | |
| -0.908 | 0.0091 | -0.03 | 0 | 0.37 | Wendepunkt W(-0.91|0.01) |
| -0.5 | 0.0013 | -0.01 | 0.05 | -0.08 | |
| 0 | 0 | 0 | 0 | 0 | Nullstelle N(0|0) = Schnittpunkt Sy(0|0) = Tiefpunkt T(0|0) |
| 0.5 | 0.0013 | 0.01 | 0.05 | 0.08 | |
| 0.906 | 0.009 | 0.03 | 0 | -0.37 | Wendepunkt W(0.91|0.01) |
| 1 | 0.0114 | 0.02 | -0.04 | -0.49 | |
| 1.226 | 0.0147 | 0 | -0.17 | -0.67 | Hochpunkt H(1.23|0.01) |
| 1.5 | 0.006 | -0.07 | -0.34 | -0.46 | |
| 1.57 | 0.0001 | -0.1 | -0.37 | -0.32 | Nullstelle N(1.57|0) |
| 2 | -0.0757 | -0.24 | -0.2 | 1.24 | |
| 2.132 | -0.1092 | -0.26 | 0 | 1.78 | Wendepunkt W(2.13|-0.11) |
| 2.5 | -0.1873 | -0.11 | 0.84 | 2.5 | |
| 2.616 | -0.1942 | 0 | 1.12 | 2.3 | Tiefpunkt T(2.62|-0.19) |
| 3 | -0.0943 | 0.55 | 1.61 | -0.2 | |
| 3.14 | -0.0012 | 0.77 | 1.48 | -1.68 | Nullstelle N(3.14|0) |
| 3.5 | 0.3521 | 1.11 | 0.15 | -5.63 | |
| 3.526 | 0.381 | 1.11 | 0 | -5.86 | Wendepunkt W(3.53|0.38) |
| 4 | 0.7915 | 0.36 | -3.22 | -6.37 | |
| 4.102 | 0.8105 | 0 | -3.82 | -5.3 | Hochpunkt H(4.1|0.81) |
| 4.5 | 0.4694 | -1.76 | -4.51 | 2.76 | |
| 4.712 | 0.001 | -2.61 | -3.33 | 8.36 | Nullstelle N(4.71|0) |
| 4.996 | -0.8375 | -3.13 | -0.01 | 14.63 | Wendepunkt W(5|-0.84) |
| 5 | -0.85 | -3.13 | 0.05 | 14.7 | |
| 5.5 | -2.0797 | -1.12 | 7.93 | 13.45 | |
| 5.628 | -2.1532 | 0 | 9.43 | 9.73 | Tiefpunkt T(5.63|-2.15) |
| 6 | -1.4487 | 3.83 | 10.11 | -7.35 | |
| 6.282 | -0.0073 | 6.19 | 5.95 | -21.97 | Nullstelle N(6.28|-0.01) |
| 6.5 | 1.4424 | 6.9 | 0.19 | -30.25 | |
| 6.506 | 1.4837 | 6.9 | 0 | -30.41 | Wendepunkt W(6.51|1.48) |
| 7 | 4.2472 | 2.99 | -15.46 | -25.98 | |
| 7.17 | 4.5131 | 0.03 | -19.08 | -15.74 | Hochpunkt H(7.17|4.51) |
| 7.5 | 3.4293 | -6.64 | -19.76 | 13.17 | |
| 7.852 | 0.024 | -12.09 | -9.34 | 44.84 | Nullstelle N(7.85|0.02) |
| 8 | -1.8426 | -12.95 | -2 | 53.9 | |
| 8.036 | -2.3096 | -12.99 | -0.03 | 55.47 | Wendepunkt W(8.04|-2.31) |
| 8.5 | -7.3802 | -6.83 | 25.93 | 46.95 | |
| 8.724 | -8.181 | -0.02 | 34 | 23.03 | Tiefpunkt T(8.72|-8.18) |
| 9 | -6.8434 | 9.75 | 34.89 | -18.31 | |
| 9.424 | -0.0163 | 20.92 | 13.39 | -79.5 | Nullstelle N(9.42|-0.02) |
| 9.5 | 1.6063 | 21.7 | 7.07 | -86.7 | |
| 9.578 | 3.3133 | 21.98 | 0.08 | -92.15 | Wendepunkt W(9.58|3.31) |
| 10 | 11.4118 | 13.63 | -38.84 | -79.87 | |
| Graph: | |||||
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Abkürzungen: Df = (maximaler) Definitionsbereich, f(x) = Funktion, f'(x) = 1. Ableitung, f''(x) = 2. Ableitung, f'''(x) = 3. Ableitung, H = Hochpunkt, L = Lücke, N = Nullstelle, P = Polstelle, R = reelle Zahlen, S = Sprungstelle, T = Tiefpunkt, W = Wendepunkt, WS = Sattelpunkt, Wf = Wertebereich, {.} = ein-/mehrelementige Menge, [.; .] = abgeschlossenes Intervall, (.; .) = offenes Intervall, [.; .), (.; .] = halboffenes Intervall, ∞ = unendlich.
Bearbeiter: Michael Buhlmann