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受欢迎的函数 >

f(x)=x^7+x^5+1/(x^3)+4x

解答

f (x) = x^{7} + x^{5} + \frac{1}{x ^{3}} + 4 x

解答

Domain : x < 0 or x > 0

Range : f (x) \leq - (\frac{6.25459 E 15}{1.0 E 16})^{\frac{7}{2}} - (\frac{6.25459 E 15}{1.0 E 16})^{\frac{5}{2}} - \frac{1.0 E 1 6 ^{3}}{6.25459 E 1 5 ^{3}} - 4 \frac{6.25459 E 15}{1.0 E 16} or f (x) \geq (\frac{6.25459 E 15}{1.0 E 16})^{\frac{7}{2}} + (\frac{6.25459 E 15}{1.0 E 16})^{\frac{5}{2}} + \frac{1.0 E 1 6 ^{3}}{6.25459 E 1 5 ^{3}} + 4 \frac{6.25459 E 15}{1.0 E 16}

Intercepts : 无

Asymptotes : 垂直 x = 0

Extreme Points : 极大值 (- \frac{6.25459 E 15}{1.0 E 16}, - (\frac{6.25459 E 15}{1.0 E 16})^{\frac{7}{2}} - (\frac{6.25459 E 15}{1.0 E 16})^{\frac{5}{2}} - \frac{1.0 E 1 6 ^{3}}{6.25459 E 1 5 ^{3}} - 4 \frac{6.25459 E 15}{1.0 E 16}), 极小值 (\frac{6.25459 E 15}{1.0 E 16}, (\frac{6.25459 E 15}{1.0 E 16})^{\frac{7}{2}} + (\frac{6.25459 E 15}{1.0 E 16})^{\frac{5}{2}} + \frac{1.0 E 1 6 ^{3}}{6.25459 E 1 5 ^{3}} + 4 \frac{6.25459 E 15}{1.0 E 16})

+1

间隔符号

Domain : (- \infty, 0) \cup (0, \infty)

Range : (- \infty, - (\frac{6.25459 E 15}{1.0 E 16})^{\frac{7}{2}} - (\frac{6.25459 E 15}{1.0 E 16})^{\frac{5}{2}} - \frac{1.0 E 1 6 ^{3}}{6.25459 E 1 5 ^{3}} - 4 \frac{6.25459 E 15}{1.0 E 16}] \cup [(\frac{6.25459 E 15}{1.0 E 16})^{\frac{7}{2}} + (\frac{6.25459 E 15}{1.0 E 16})^{\frac{5}{2}} + \frac{1.0 E 1 6 ^{3}}{6.25459 E 1 5 ^{3}} + 4 \frac{6.25459 E 15}{1.0 E 16}, \infty)

求解步骤

x^{7} + x^{5} + \frac{1}{x ^{3}} + 4 x

的定义域

: x < 0 or x > 0

x^{7} + x^{5} + \frac{1}{x ^{3}} + 4 x

的值域:

f (x) \leq - (\frac{6.25459 E 15}{1.0 E 16})^{\frac{7}{2}} - (\frac{6.25459 E 15}{1.0 E 16})^{\frac{5}{2}} - \frac{1.0 E 1 6 ^{3}}{6.25459 E 1 5 ^{3}} - 4 \frac{6.25459 E 15}{1.0 E 16} or f (x) \geq (\frac{6.25459 E 15}{1.0 E 16})^{\frac{7}{2}} + (\frac{6.25459 E 15}{1.0 E 16})^{\frac{5}{2}} + \frac{1.0 E 1 6 ^{3}}{6.25459 E 1 5 ^{3}} + 4 \frac{6.25459 E 15}{1.0 E 16}

x^{7} + x^{5} + \frac{1}{x ^{3}} + 4 x

的轴截距点

:

无

x^{7} + x^{5} + \frac{1}{x ^{3}} + 4 x

的渐近线

:

垂直

: x = 0

x^{7} + x^{5} + \frac{1}{x ^{3}} + 4 x

的极值点:

极大值

(- \frac{6.25459 E 15}{1.0 E 16}, - (\frac{6.25459 E 15}{1.0 E 16})^{\frac{7}{2}} - (\frac{6.25459 E 15}{1.0 E 16})^{\frac{5}{2}} - \frac{1.0 E 1 6 ^{3}}{6.25459 E 1 5 ^{3}} - 4 \frac{6.25459 E 15}{1.0 E 16}),

极小值

(\frac{6.25459 E 15}{1.0 E 16}, (\frac{6.25459 E 15}{1.0 E 16})^{\frac{7}{2}} + (\frac{6.25459 E 15}{1.0 E 16})^{\frac{5}{2}} + \frac{1.0 E 1 6 ^{3}}{6.25459 E 1 5 ^{3}} + 4 \frac{6.25459 E 15}{1.0 E 16})

作图

流行的例子

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f (x) = cos (x) + x

y = \frac{x}{( x - 1 ) ^{2}}

y = 25 x