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受欢迎的函数 >

extreme f(x)=x^{11}-9x^7+5x-3

解答

极值点

f (x) = x^{11} - 9 x^{7} + 5 x - 3

解答

极大值 (- \frac{5.96543 E 15}{2.5 E 15}, - (\frac{5.96543 E 15}{2.5 E 15})^{\frac{11}{2}} + 9 (\frac{5.96543 E 15}{2.5 E 15})^{\frac{7}{2}} - 5 \frac{5.96543 E 15}{2.5 E 15} - 3), 极小值 (- \frac{4.34574 E 15}{1.0 E 16}, - (\frac{4.34574 E 15}{1.0 E 16})^{\frac{11}{2}} + 9 (\frac{4.34574 E 15}{1.0 E 16})^{\frac{7}{2}} - 5 \frac{4.34574 E 15}{1.0 E 16} - 3), 极大值 (\frac{4.34574 E 15}{1.0 E 16}, (\frac{4.34574 E 15}{1.0 E 16})^{\frac{11}{2}} - 9 (\frac{4.34574 E 15}{1.0 E 16})^{\frac{7}{2}} + 5 \frac{4.34574 E 15}{1.0 E 16} - 3), 极小值 (\frac{5.96543 E 15}{2.5 E 15}, (\frac{5.96543 E 15}{2.5 E 15})^{\frac{11}{2}} - 9 (\frac{5.96543 E 15}{2.5 E 15})^{\frac{7}{2}} + 5 \frac{5.96543 E 15}{2.5 E 15} - 3)

求解步骤

找到临界点:

x = - \frac{5.96543 E 15}{2.5 E 15}, x = - \frac{4.34574 E 15}{1.0 E 16}, x = \frac{4.34574 E 15}{1.0 E 16}, x = \frac{5.96543 E 15}{2.5 E 15}

x^{11} - 9 x^{7} + 5 x - 3

的定义域

: - \infty < x < \infty

Find intervals:

递增

: - \infty < x < - \frac{5.96543 E 15}{2.5 E 15},

递减

: - \frac{5.96543 E 15}{2.5 E 15} < x < - \frac{4.34574 E 15}{1.0 E 16},

递增

: - \frac{4.34574 E 15}{1.0 E 16} < x < \frac{4.34574 E 15}{1.0 E 16},

递减

: \frac{4.34574 E 15}{1.0 E 16} < x < \frac{5.96543 E 15}{2.5 E 15},

递增

: \frac{5.96543 E 15}{2.5 E 15} < x < \infty

将极值点

x = - \frac{5.96543 E 15}{2.5 E 15}

代入

x^{11} - 9 x^{7} + 5 x - 3 \Rightarrow y = - (\frac{5.96543 E 15}{2.5 E 15})^{\frac{11}{2}} + 9 (\frac{5.96543 E 15}{2.5 E 15})^{\frac{7}{2}} - 5 \frac{5.96543 E 15}{2.5 E 15} - 3

极大值 (- \frac{5.96543 E 15}{2.5 E 15}, - (\frac{5.96543 E 15}{2.5 E 15})^{\frac{11}{2}} + 9 (\frac{5.96543 E 15}{2.5 E 15})^{\frac{7}{2}} - 5 \frac{5.96543 E 15}{2.5 E 15} - 3)

将极值点

x = - \frac{4.34574 E 15}{1.0 E 16}

代入

x^{11} - 9 x^{7} + 5 x - 3 \Rightarrow y = - (\frac{4.34574 E 15}{1.0 E 16})^{\frac{11}{2}} + 9 (\frac{4.34574 E 15}{1.0 E 16})^{\frac{7}{2}} - 5 \frac{4.34574 E 15}{1.0 E 16} - 3

极小值 (- \frac{4.34574 E 15}{1.0 E 16}, - (\frac{4.34574 E 15}{1.0 E 16})^{\frac{11}{2}} + 9 (\frac{4.34574 E 15}{1.0 E 16})^{\frac{7}{2}} - 5 \frac{4.34574 E 15}{1.0 E 16} - 3)

将极值点

x = \frac{4.34574 E 15}{1.0 E 16}

代入

x^{11} - 9 x^{7} + 5 x - 3 \Rightarrow y = (\frac{4.34574 E 15}{1.0 E 16})^{\frac{11}{2}} - 9 (\frac{4.34574 E 15}{1.0 E 16})^{\frac{7}{2}} + 5 \frac{4.34574 E 15}{1.0 E 16} - 3

极大值 (\frac{4.34574 E 15}{1.0 E 16}, (\frac{4.34574 E 15}{1.0 E 16})^{\frac{11}{2}} - 9 (\frac{4.34574 E 15}{1.0 E 16})^{\frac{7}{2}} + 5 \frac{4.34574 E 15}{1.0 E 16} - 3)

将极值点

x = \frac{5.96543 E 15}{2.5 E 15}

代入

x^{11} - 9 x^{7} + 5 x - 3 \Rightarrow y = (\frac{5.96543 E 15}{2.5 E 15})^{\frac{11}{2}} - 9 (\frac{5.96543 E 15}{2.5 E 15})^{\frac{7}{2}} + 5 \frac{5.96543 E 15}{2.5 E 15} - 3

极小值 (\frac{5.96543 E 15}{2.5 E 15}, (\frac{5.96543 E 15}{2.5 E 15})^{\frac{11}{2}} - 9 (\frac{5.96543 E 15}{2.5 E 15})^{\frac{7}{2}} + 5 \frac{5.96543 E 15}{2.5 E 15} - 3)

极大值 (- \frac{5.96543 E 15}{2.5 E 15}, - (\frac{5.96543 E 15}{2.5 E 15})^{\frac{11}{2}} + 9 (\frac{5.96543 E 15}{2.5 E 15})^{\frac{7}{2}} - 5 \frac{5.96543 E 15}{2.5 E 15} - 3), 极小值 (- \frac{4.34574 E 15}{1.0 E 16}, - (\frac{4.34574 E 15}{1.0 E 16})^{\frac{11}{2}} + 9 (\frac{4.34574 E 15}{1.0 E 16})^{\frac{7}{2}} - 5 \frac{4.34574 E 15}{1.0 E 16} - 3), 极大值 (\frac{4.34574 E 15}{1.0 E 16}, (\frac{4.34574 E 15}{1.0 E 16})^{\frac{11}{2}} - 9 (\frac{4.34574 E 15}{1.0 E 16})^{\frac{7}{2}} + 5 \frac{4.34574 E 15}{1.0 E 16} - 3), 极小值 (\frac{5.96543 E 15}{2.5 E 15}, (\frac{5.96543 E 15}{2.5 E 15})^{\frac{11}{2}} - 9 (\frac{5.96543 E 15}{2.5 E 15})^{\frac{7}{2}} + 5 \frac{5.96543 E 15}{2.5 E 15} - 3)

作图

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