www.michael-buhlmann.de
Funktion: f(x) = x4/4 + 2x3/3 - 14.5·x2 - 30x + 38.25, Df = R, Wf = [-234 2/3; +∞), Polynom 4. Grades, x -> -∞: f(x) -> +∞, x -> +∞: f(x) -> +∞ ->
Wertetabelle: | |||||
x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
-20 | 29504.9167 | -6650 | 1091 | -116 | |
-19.5 | 26313.8906 | -6118.88 | 1033.75 | -113 | |
-19 | 23381.3333 | -5616 | 978 | -110 | |
-18.5 | 20693.3073 | -5140.63 | 923.75 | -106.99 | |
-18 | 18236.25 | -4692 | 871 | -104 | |
-17.5 | 15996.974 | -4269.38 | 819.75 | -101 | |
-17 | 13962.6667 | -3872 | 770 | -98 | |
-16.5 | 12120.8906 | -3499.13 | 721.75 | -95 | |
-16 | 10459.5833 | -3150 | 675 | -92 | |
-15.5 | 8967.0573 | -2823.88 | 629.75 | -88.99 | |
-15 | 7632 | -2520 | 586 | -86 | |
-14.5 | 6443.474 | -2237.63 | 543.75 | -82.99 | |
-14 | 5390.9167 | -1976 | 503 | -80 | |
-13.5 | 4464.1406 | -1734.38 | 463.75 | -77 | |
-13 | 3653.3333 | -1512 | 426 | -73.99 | |
-12.5 | 2949.0573 | -1308.13 | 389.75 | -70.99 | |
-12 | 2342.25 | -1122 | 355 | -67.99 | |
-11.5 | 1824.224 | -952.88 | 321.75 | -64.99 | |
-11 | 1386.6667 | -800 | 290 | -61.99 | |
-10.5 | 1021.6406 | -662.63 | 259.75 | -58.99 | |
-10 | 721.5833 | -540 | 231 | -55.99 | |
-9.5 | 479.3073 | -431.38 | 203.75 | -52.99 | |
-9 | 288 | -336 | 178 | -49.99 | |
-8.5 | 141.224 | -253.13 | 153.75 | -46.99 | |
-8 | 32.9167 | -182 | 131 | -43.99 | |
-7.806 | 0 | -157.41 | 122.58 | -42.83 | Nullstelle N(-7.81|0) |
-7.5 | -42.6094 | -121.88 | 109.75 | -40.99 | |
-7 | -90.6667 | -72 | 90 | -37.99 | |
-6.5 | -116.1927 | -31.63 | 71.75 | -34.99 | |
-6 | -123.75 | 0 | 55 | -31.99 | Tiefpunkt T(-6|-123.75) |
-5.5 | -117.526 | 23.62 | 39.75 | -28.99 | |
-5 | -101.3333 | 40 | 26 | -25.99 | |
-4.5 | -78.6094 | 49.87 | 13.75 | -22.99 | |
-4 | -52.4167 | 54 | 3 | -19.99 | |
-3.848 | -44.1856 | 54.23 | 0 | -19.08 | Wendepunkt W(-3.85|-44.19) |
-3.5 | -25.4427 | 53.12 | -6.25 | -16.99 | |
-3 | 0 | 48 | -14 | -13.99 | Nullstelle N(-3|0) |
-2.5 | 21.974 | 39.37 | -20.25 | -10.99 | |
-2 | 38.9167 | 28 | -25 | -7.99 | |
-1.5 | 49.6406 | 14.62 | -28.25 | -4.99 | |
-1 | 53.3333 | 0 | -30 | -1.99 | Hochpunkt H(-1|53.33) |
-0.5 | 49.5573 | -15.12 | -30.25 | 1.01 | |
0 | 38.25 | -30 | -29 | 4.01 | Schnittpunkt Sy(0|38.25) |
0.5 | 19.724 | -43.87 | -26.25 | 7.01 | |
0.902 | 0 | -53.8 | -22.95 | 9.42 | Nullstelle N(0.9|0) |
1 | -5.3333 | -56 | -22 | 10.01 | |
1.5 | -35.8594 | -65.62 | -16.25 | 13.01 | |
2 | -70.4167 | -72 | -9 | 16.01 | |
2.5 | -107.1927 | -74.37 | -0.25 | 19.01 | |
2.512 | -108.0852 | -74.38 | 0 | 19.08 | Wendepunkt W(2.51|-108.09) |
3 | -144 | -72 | 10 | 22.01 | |
3.5 | -178.276 | -64.12 | 21.75 | 25.01 | |
4 | -207.0833 | -50 | 35 | 28.01 | |
4.5 | -227.1094 | -28.87 | 49.75 | 31.01 | |
5 | -234.6667 | 0 | 66 | 34.01 | Tiefpunkt T(5|-234.67) |
5.5 | -225.6927 | 37.38 | 83.75 | 37.01 | |
6 | -195.75 | 84 | 103 | 40.01 | |
6.5 | -140.026 | 140.63 | 123.75 | 43.01 | |
7 | -53.3333 | 208 | 146 | 46.01 | |
7.236 | 0 | 243.75 | 157.02 | 47.42 | Nullstelle N(7.24|0) |
7.5 | 69.8906 | 286.88 | 169.75 | 49.01 | |
8 | 235.5833 | 378 | 195 | 52.01 | |
8.5 | 450.0573 | 482.13 | 221.75 | 55.01 | |
9 | 720 | 600 | 250 | 58.01 | |
9.5 | 1052.474 | 732.38 | 279.75 | 61.01 | |
10 | 1454.9167 | 880 | 311 | 64.01 | |
10.5 | 1935.1406 | 1043.63 | 343.75 | 67.01 | |
11 | 2501.3333 | 1224 | 378 | 70.01 | |
11.5 | 3162.0573 | 1421.88 | 413.75 | 73.01 | |
12 | 3926.25 | 1638 | 451 | 76.01 | |
12.5 | 4803.224 | 1873.13 | 489.75 | 79 | |
13 | 5802.6667 | 2128 | 530 | 82.01 | |
13.5 | 6934.6406 | 2403.38 | 571.75 | 85 | |
14 | 8209.5833 | 2700 | 615 | 88.01 | |
14.5 | 9638.3073 | 3018.63 | 659.75 | 91 | |
15 | 11232 | 3360 | 706 | 94 | |
15.5 | 13002.224 | 3724.88 | 753.75 | 97 | |
16 | 14960.9167 | 4114 | 803 | 100.01 | |
16.5 | 17120.3906 | 4528.13 | 853.75 | 103.01 | |
17 | 19493.3333 | 4968 | 906 | 106.01 | |
17.5 | 22092.8073 | 5434.38 | 959.75 | 109.01 | |
18 | 24932.25 | 5928 | 1015 | 112.01 | |
18.5 | 28025.474 | 6449.63 | 1071.75 | 115.01 | |
19 | 31386.6667 | 7000 | 1130 | 118.01 | |
19.5 | 35030.3906 | 7579.88 | 1189.75 | 121.01 | |
20 | 38971.5833 | 8190 | 1251 | 124.01 | |
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