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Beliebt Funktionen >

Q(a)=a^{12}-6a^8+5a^4+2a^6-6a^2+1

Lösung

Q (a) = a^{12} - 6 a^{8} + 5 a^{4} + 2 a^{6} - 6 a^{2} + 1

Lösung

Domain : - \infty < a < \infty

Range : f (x) \geq - \frac{1.1897 E 15}{1.25 E 14} + \frac{8.76468 E 1 5 ^{6}}{5.0 E 1 5 ^{6}} - \frac{8.76468 E 1 5 ^{4} \cdot 6}{5.0 E 1 5 ^{4}} + \frac{8.76468 E 1 5 ^{2} \cdot 5}{5.0 E 1 5 ^{2}} + \frac{8.76468 E 1 5 ^{3} \cdot 2}{5.0 E 1 5 ^{3}}

X - Schnittpunkte : (0.20163 \dots, 0), (- 0.20163 \dots, 0), (2.12841 \dots, 0), (- 2.12841 \dots, 0), Y - Schnittpunkte : (0, 1)

Asymptotes : Horizontal y = a^{12} - 6 a^{8} + 5 a^{4} + 2 a^{6} - 6 a^{2} + 1

Extreme Points : Minimum (- \frac{8.76468 E 15}{5.0 E 15}, - \frac{1.1897 E 15}{1.25 E 14} + \frac{8.76468 E 1 5 ^{6}}{5.0 E 1 5 ^{6}} - \frac{8.76468 E 1 5 ^{4} \cdot 6}{5.0 E 1 5 ^{4}} + \frac{8.76468 E 1 5 ^{2} \cdot 5}{5.0 E 1 5 ^{2}} + \frac{8.76468 E 1 5 ^{3} \cdot 2}{5.0 E 1 5 ^{3}}), Maximum (0, 1), Minimum (\frac{8.76468 E 15}{5.0 E 15}, - \frac{1.1897 E 15}{1.25 E 14} + \frac{8.76468 E 1 5 ^{6}}{5.0 E 1 5 ^{6}} - \frac{8.76468 E 1 5 ^{4} \cdot 6}{5.0 E 1 5 ^{4}} + \frac{8.76468 E 1 5 ^{2} \cdot 5}{5.0 E 1 5 ^{2}} + \frac{8.76468 E 1 5 ^{3} \cdot 2}{5.0 E 1 5 ^{3}})

+1

Intervall-Notation

Domain : (- \infty, \infty)

Range : [- \frac{1.1897 E 15}{1.25 E 14} + \frac{8.76468 E 1 5 ^{6}}{5.0 E 1 5 ^{6}} - \frac{8.76468 E 1 5 ^{4} 6}{5.0 E 1 5 ^{4}} + \frac{8.76468 E 1 5 ^{2} 5}{5.0 E 1 5 ^{2}} + \frac{8.76468 E 1 5 ^{3} 2}{5.0 E 1 5 ^{3}}, \infty)

Schritte zur Lösung

Bereich von

a^{12} - 6 a^{8} + 5 a^{4} + 2 a^{6} - 6 a^{2} + 1 : - \infty < a < \infty

Bereich von

a^{12} - 6 a^{8} + 5 a^{4} + 2 a^{6} - 6 a^{2} + 1 : f (x) \geq - \frac{1.1897 E 15}{1.25 E 14} + \frac{8.76468 E 1 5 ^{6}}{5.0 E 1 5 ^{6}} - \frac{8.76468 E 1 5 ^{4} \cdot 6}{5.0 E 1 5 ^{4}} + \frac{8.76468 E 1 5 ^{2} \cdot 5}{5.0 E 1 5 ^{2}} + \frac{8.76468 E 1 5 ^{3} \cdot 2}{5.0 E 1 5 ^{3}}

Schnittpunkte mit der Achse von

a^{12} - 6 a^{8} + 5 a^{4} + 2 a^{6} - 6 a^{2} + 1 :

X-Schnittpunkte

: (0.20163 \dots, 0), (- 0.20163 \dots, 0), (2.12841 \dots, 0), (- 2.12841 \dots, 0),

Y-Schnittpunkte

: (0, 1)

Asymptoten von

a^{12} - 6 a^{8} + 5 a^{4} + 2 a^{6} - 6 a^{2} + 1 :

Horizontal

: y = a^{12} - 6 a^{8} + 5 a^{4} + 2 a^{6} - 6 a^{2} + 1

Extrempunkte vonf

a^{12} - 6 a^{8} + 5 a^{4} + 2 a^{6} - 6 a^{2} + 1 :

Minimum

(- \frac{8.76468 E 15}{5.0 E 15}, - \frac{1.1897 E 15}{1.25 E 14} + \frac{8.76468 E 1 5 ^{6}}{5.0 E 1 5 ^{6}} - \frac{8.76468 E 1 5 ^{4} \cdot 6}{5.0 E 1 5 ^{4}} + \frac{8.76468 E 1 5 ^{2} \cdot 5}{5.0 E 1 5 ^{2}} + \frac{8.76468 E 1 5 ^{3} \cdot 2}{5.0 E 1 5 ^{3}}),

Maximum

(0, 1),

Minimum

(\frac{8.76468 E 15}{5.0 E 15}, - \frac{1.1897 E 15}{1.25 E 14} + \frac{8.76468 E 1 5 ^{6}}{5.0 E 1 5 ^{6}} - \frac{8.76468 E 1 5 ^{4} \cdot 6}{5.0 E 1 5 ^{4}} + \frac{8.76468 E 1 5 ^{2} \cdot 5}{5.0 E 1 5 ^{2}} + \frac{8.76468 E 1 5 ^{3} \cdot 2}{5.0 E 1 5 ^{3}})

Graph

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