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受欢迎的函数 >

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

解答

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

解答

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

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

Extreme Points : 极小值 (- \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}}), 极大值 (0, 1), 极小值 (\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

间隔符号

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)

求解步骤

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

的定义域

: - \infty < a < \infty

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

的值域:

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}}

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

的轴截距点

:

X 截距

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

Y 截距

: (0, 1)

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

的渐近线

:

水平

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

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

的极值点:

极小值

(- \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}}),

极大值

(0, 1),

极小值

(\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}})

作图

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