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Funktion: f(x) = x4/4 + x3/3 + 18x, Df = R, Wf = [-42.75; ∞), Polynom 4. Grades, x -> -∞: f(x) -> +∞, x -> +∞: f(x) -> +∞ ->
Wertetabelle: | |||||
x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
-10 | 1986.6667 | -882 | 280 | -58 | |
-9.5 | 1579.474 | -749.13 | 251.75 | -55 | |
-9 | 1235.25 | -630 | 225 | -52 | |
-8.5 | 947.3073 | -523.88 | 199.75 | -49 | |
-8 | 709.3333 | -430 | 176 | -46 | |
-7.5 | 515.3906 | -347.63 | 153.75 | -43 | |
-7 | 359.9167 | -276 | 133 | -40 | |
-6.5 | 237.724 | -214.38 | 113.75 | -37 | |
-6 | 144 | -162 | 96 | -34 | |
-5.5 | 74.3073 | -118.13 | 79.75 | -31 | |
-5 | 24.5833 | -82 | 65 | -28 | |
-4.656 | 0 | -61.26 | 55.72 | -25.93 | Nullstelle N(-4.66|0.03) |
-4.5 | -8.8594 | -52.88 | 51.75 | -25 | |
-4 | -29.3333 | -30 | 40 | -22 | |
-3.5 | -39.776 | -12.63 | 29.75 | -19 | |
-3 | -42.75 | 0 | 21 | -16 | Tiefpunkt T(-3|-42.75) |
-2.5 | -40.4427 | 8.62 | 13.75 | -13 | |
-2 | -34.6667 | 14 | 8 | -10 | |
-1.5 | -26.8594 | 16.87 | 3.75 | -7 | |
-1 | -18.0833 | 18 | 1 | -4 | |
-0.667 | -12.0554 | 18.15 | 0 | -2 | Wendepunkt W(-0.67|-12.06) |
-0.5 | -9.026 | 18.12 | -0.25 | -1 | |
0 | 0 | 18 | 0 | 2 | Nullstelle N(0|0) = Schnittpunkt Sy(0|0) = Wendepunkt W(0|0) |
0.5 | 9.0573 | 18.38 | 1.75 | 5 | |
1 | 18.5833 | 20 | 5 | 8 | |
1.5 | 29.3906 | 23.63 | 9.75 | 11 | |
2 | 42.6667 | 30 | 16 | 14 | |
2.5 | 59.974 | 39.88 | 23.75 | 17 | |
3 | 83.25 | 54 | 33 | 20 | |
3.5 | 114.8073 | 73.13 | 43.75 | 23 | |
4 | 157.3333 | 98 | 56 | 26 | |
4.5 | 213.8906 | 129.38 | 69.75 | 29 | |
5 | 287.9167 | 168 | 85 | 32 | |
5.5 | 383.224 | 214.63 | 101.75 | 35 | |
6 | 504 | 270 | 120 | 38 | |
6.5 | 654.8073 | 334.88 | 139.75 | 41 | |
7 | 840.5833 | 410 | 161 | 44 | |
7.5 | 1066.6406 | 496.13 | 183.75 | 47 | |
8 | 1338.6667 | 594 | 208 | 50 | |
8.5 | 1662.724 | 704.38 | 233.75 | 53 | |
9 | 2045.25 | 828 | 261 | 56 | |
9.5 | 2493.0573 | 965.63 | 289.75 | 59 | |
10 | 3013.3333 | 1118 | 320 | 62.01 | |
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