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Funktion: f(x) = x4 - 15x3 + 6x2 - 20x + 10, Df = R, Wf = [-4808.085; +∞), Polynom 4. Grades, x -> -∞: f(x) -> +∞, x -> +∞: f(x) -> +∞ ->
| Wertetabelle: | |||||
| x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
| -20 | 282810 | -50260.01 | 6612 | -569.88 | |
| -19.5 | 258494.6875 | -47024.76 | 6330 | -557.88 | |
| -19 | 235762 | -43929.01 | 6054 | -545.88 | |
| -18.5 | 214542.9375 | -40969.76 | 5784 | -533.88 | |
| -18 | 194770 | -38144.01 | 5520 | -521.88 | |
| -17.5 | 176377.1875 | -35448.76 | 5262 | -509.88 | |
| -17 | 159300 | -32881.01 | 5010 | -497.88 | |
| -16.5 | 143475.4375 | -30437.76 | 4764 | -485.88 | |
| -16 | 128842 | -28116.01 | 4524 | -473.88 | |
| -15.5 | 115339.6875 | -25912.76 | 4290 | -461.88 | |
| -15 | 102910 | -23825.01 | 4062 | -449.88 | |
| -14.5 | 91495.9375 | -21849.76 | 3840 | -437.88 | |
| -14 | 81042 | -19984.01 | 3624 | -425.88 | |
| -13.5 | 71494.1875 | -18224.76 | 3414 | -413.88 | |
| -13 | 62800 | -16569.01 | 3210 | -401.88 | |
| -12.5 | 54908.4375 | -15013.76 | 3012 | -389.88 | |
| -12 | 47770 | -13556.01 | 2820 | -377.88 | |
| -11.5 | 41336.6875 | -12192.76 | 2634 | -365.88 | |
| -11 | 35562 | -10921.01 | 2454 | -353.88 | |
| -10.5 | 30400.9375 | -9737.76 | 2280 | -341.88 | |
| -10 | 25810 | -8640.01 | 2112 | -329.88 | |
| -9.5 | 21747.1875 | -7624.76 | 1950 | -317.88 | |
| -9 | 18172 | -6689.01 | 1794 | -305.88 | |
| -8.5 | 15045.4375 | -5829.75 | 1644 | -293.88 | |
| -8 | 12330 | -5044 | 1500 | -281.88 | |
| -7.5 | 9989.6875 | -4328.75 | 1362 | -269.88 | |
| -7 | 7990 | -3681 | 1230 | -257.88 | |
| -6.5 | 6297.9375 | -3097.75 | 1104 | -245.88 | |
| -6 | 4882 | -2576 | 984 | -233.88 | |
| -5.5 | 3712.1875 | -2112.75 | 870 | -221.88 | |
| -5 | 2760 | -1705 | 762 | -209.88 | |
| -4.5 | 1998.4375 | -1349.75 | 660 | -197.88 | |
| -4 | 1402 | -1044 | 564 | -185.88 | |
| -3.5 | 946.6875 | -784.75 | 474 | -173.88 | |
| -3 | 610 | -569 | 390 | -161.88 | |
| -2.5 | 370.9375 | -393.75 | 312 | -149.88 | |
| -2 | 210 | -256 | 240 | -137.88 | |
| -1.5 | 109.1875 | -152.75 | 174 | -125.88 | |
| -1 | 52 | -81 | 114 | -113.88 | |
| -0.5 | 23.4375 | -37.75 | 60 | -101.88 | |
| 0 | 10 | -20 | 12 | -89.88 | Schnittpunkt Sy(0|10) |
| 0.13 | 7.4687 | -19.19 | 0 | -86.76 | Wendepunkt W(0.13|7.47) |
| 0.48 | 0 | -24.17 | -28.44 | -78.36 | Nullstelle N(0.48|0) |
| 0.5 | -0.3125 | -24.75 | -30 | -77.88 | |
| 1 | -18 | -49 | -66 | -65.88 | |
| 1.5 | -52.0625 | -89.75 | -96 | -53.88 | |
| 2 | -110 | -144 | -120 | -41.88 | |
| 2.5 | -197.8125 | -208.75 | -138 | -29.88 | |
| 3 | -320 | -281 | -150 | -17.88 | |
| 3.5 | -479.5625 | -357.75 | -156 | -5.88 | |
| 4 | -678 | -436 | -156 | 6.12 | |
| 4.5 | -915.3125 | -512.75 | -150 | 18.12 | |
| 5 | -1190 | -585 | -138 | 30.12 | |
| 5.5 | -1499.0625 | -649.75 | -120 | 42.12 | |
| 6 | -1838 | -704 | -96 | 54.12 | |
| 6.5 | -2200.8125 | -744.75 | -66 | 66.12 | |
| 7 | -2580 | -769 | -30 | 78.12 | |
| 7.36 | -2858.1607 | -774.56 | 0 | 86.76 | Wendepunkt W(7.36|-2858.16) |
| 7.5 | -2966.5625 | -773.75 | 12 | 90.12 | |
| 8 | -3350 | -756 | 60 | 102.12 | |
| 8.5 | -3718.3125 | -712.75 | 114 | 114.12 | |
| 9 | -4058 | -641 | 174 | 126.12 | |
| 9.5 | -4354.0625 | -537.75 | 240 | 138.12 | |
| 10 | -4590 | -400 | 312 | 150.12 | |
| 10.5 | -4747.8125 | -224.75 | 390 | 162.12 | |
| 11 | -4808 | -9 | 474 | 174.12 | |
| 11.018 | -4808.085 | 0 | 475.74 | 174.36 | Tiefpunkt T(11.02|-4808.09) |
| 11.5 | -4749.5625 | 250.25 | 564 | 186.12 | |
| 12 | -4550 | 556 | 660 | 198.12 | |
| 12.5 | -4185.3125 | 911.25 | 762 | 210.12 | |
| 13 | -3630 | 1319 | 870 | 222.12 | |
| 13.5 | -2857.0625 | 1782.25 | 984 | 234.12 | |
| 14 | -1838 | 2304 | 1104 | 246.12 | |
| 14.5 | -542.8125 | 2887.25 | 1230 | 258.12 | |
| 14.68 | 0 | 3112.86 | 1276.83 | 262.44 | Nullstelle N(14.68|0) |
| 15 | 1060 | 3535 | 1362 | 270.12 | |
| 15.5 | 3003.4375 | 4250.25 | 1500 | 282.12 | |
| 16 | 5322 | 5036 | 1644 | 294.12 | |
| 16.5 | 8051.6875 | 5895.26 | 1794 | 306.12 | |
| 17 | 11230 | 6831.01 | 1950 | 318.12 | |
| 17.5 | 14895.9375 | 7846.26 | 2112 | 330.12 | |
| 18 | 19090 | 8944.01 | 2280 | 342.12 | |
| 18.5 | 23854.1875 | 10127.26 | 2454 | 354.12 | |
| 19 | 29232 | 11399.01 | 2634 | 366.12 | |
| 19.5 | 35268.4375 | 12762.26 | 2820 | 378.12 | |
| 20 | 42010 | 14220.01 | 3012 | 390.12 | |
| 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, 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