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Funktion: f(x) = x·sin(πx/2), 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 | 0 | 15.71 | -3.14 | -38.75 | Nullstelle N(-10|0) |
| -9.5 | 6.7175 | 9.84 | -18.8 | -20.78 | |
| -9.045 | 9.0224 | 0.01 | -22.48 | 4.94 | Hochpunkt H(-9.04|9.02) |
| -9 | 9 | -1 | -22.21 | 7.43 | |
| -8.5 | 6.0104 | -10.15 | -12.61 | 28.54 | |
| -8.1 | 1.2671 | -12.72 | -0.02 | 32.16 | Wendepunkt W(-8.1|1.27) |
| -8 | 0 | -12.57 | 3.14 | 31 | Nullstelle N(-8|0) |
| -7.5 | -5.3033 | -7.62 | 15.31 | 15.3 | |
| -7.058 | -7.0287 | -0.01 | 17.63 | -4.9 | Tiefpunkt T(-7.06|-7.03) |
| -7 | -7 | 1 | 17.27 | -7.42 | |
| -6.5 | -4.5962 | 7.93 | 9.12 | -23.06 | |
| -6.131 | -1.2527 | 9.63 | 0.02 | -24.77 | Wendepunkt W(-6.13|-1.25) |
| -6 | 0 | 9.42 | -3.14 | -23.25 | Nullstelle N(-6|0) |
| -5.5 | 3.8891 | 5.4 | -11.82 | -9.82 | |
| -5.08 | 5.0399 | 0.01 | -12.83 | 4.89 | Hochpunkt H(-5.08|5.04) |
| -5 | 5 | -1 | -12.34 | 7.42 | |
| -4.5 | 3.182 | -5.71 | -5.63 | 17.57 | |
| -4.188 | 1.2189 | -6.58 | 0 | 17.68 | Wendepunkt W(-4.19|1.22) |
| -4 | 0 | -6.28 | 3.14 | 15.5 | Nullstelle N(-4|0) |
| -3.5 | -2.4749 | -3.18 | 8.33 | 4.34 | |
| -3.128 | -3.065 | 0 | 8.19 | -4.84 | Tiefpunkt T(-3.13|-3.06) |
| -3 | -3 | 1 | 7.4 | -7.41 | |
| -2.5 | -1.7678 | 3.48 | 2.14 | -12.09 | |
| -2.32 | -1.1177 | 3.68 | 0 | -11.44 | Wendepunkt W(-2.32|-1.12) |
| -2 | 0 | 3.14 | -3.14 | -7.74 | Nullstelle N(-2|0) |
| -1.5 | 1.0607 | 0.96 | -4.84 | 1.13 | |
| -1.292 | 1.1585 | 0 | -4.25 | 4.43 | Hochpunkt H(-1.29|1.16) |
| -1 | 1 | -1 | -2.47 | 7.41 | |
| -0.686 | 0.6042 | -1.39 | 0 | 7.78 | Wendepunkt W(-0.69|0.6) |
| -0.5 | 0.3536 | -1.26 | 1.35 | 6.6 | |
| 0 | 0 | 0 | 3.14 | -0.01 | Nullstelle N(0|0) = Schnittpunkt Sy(0|0) = Tiefpunkt T(0|0) |
| 0.5 | 0.3536 | 1.26 | 1.35 | -6.61 | |
| 0.685 | 0.6028 | 1.39 | 0 | -7.78 | Wendepunkt W(0.69|0.6) |
| 1 | 1 | 1 | -2.47 | -7.4 | |
| 1.291 | 1.1585 | 0 | -4.24 | -4.43 | Hochpunkt H(1.29|1.16) |
| 1.5 | 1.0607 | -0.96 | -4.84 | -1.11 | |
| 2 | 0 | -3.14 | -3.14 | 7.76 | Nullstelle N(2|0) |
| 2.319 | -1.114 | -3.68 | -0.01 | 11.44 | Wendepunkt W(2.32|-1.11) |
| 2.5 | -1.7678 | -3.48 | 2.14 | 12.09 | |
| 3 | -3 | -1 | 7.4 | 7.39 | |
| 3.127 | -3.065 | -0.01 | 8.19 | 4.84 | Tiefpunkt T(3.13|-3.06) |
| 3.5 | -2.4749 | 3.18 | 8.33 | -4.37 | |
| 4 | 0 | 6.28 | 3.14 | -15.51 | Nullstelle N(4|0) |
| 4.187 | 1.2123 | 6.58 | 0.02 | -17.68 | Wendepunkt W(4.19|1.21) |
| 4.5 | 3.182 | 5.71 | -5.63 | -17.56 | |
| 5 | 5 | 1 | -12.34 | -7.39 | |
| 5.079 | 5.0399 | 0 | -12.82 | -4.89 | Hochpunkt H(5.08|5.04) |
| 5.5 | 3.8891 | -5.4 | -11.82 | 9.86 | |
| 6 | 0 | -9.42 | -3.14 | 23.26 | Nullstelle N(6|0) |
| 6.13 | -1.2431 | -9.63 | -0.01 | 24.77 | Wendepunkt W(6.13|-1.24) |
| 6.5 | -4.5962 | -7.93 | 9.12 | 23.04 | |
| 7 | -7 | -1 | 17.27 | 7.38 | |
| 7.057 | -7.0287 | 0 | 17.62 | 4.9 | Tiefpunkt T(7.06|-7.03) |
| 7.5 | -5.3033 | 7.62 | 15.31 | -15.34 | |
| 8 | 0 | 12.57 | 3.14 | -31.01 | Nullstelle N(8|0) |
| 8.099 | 1.2544 | 12.72 | 0.01 | -32.16 | Wendepunkt W(8.1|1.25) |
| 8.5 | 6.0104 | 10.15 | -12.61 | -28.52 | |
| 9 | 9 | 1 | -22.21 | -7.37 | |
| 9.044 | 9.0224 | 0.02 | -22.48 | -4.94 | Hochpunkt H(9.04|9.02) |
| 9.5 | 6.7175 | -9.84 | -18.8 | 20.83 | |
| 10 | 0 | -15.71 | -3.14 | 38.77 | Nullstelle N(10|0) |
| 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