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人気のある関数 >

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

解

端点

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

解

最大値 (- \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), 最小値 (- \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), 最大値 (\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), 最小値 (\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)

解答ステップ

臨界点を求める:

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}

以下の領域:

x^{11} - 9 x^{7} + 5 x - 3 : - \infty < x < \infty

区間を求める:

増加中

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

減少中

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

増加中

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

減少中

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

増加中

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

極点

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

を以下に当てはめる:

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

最大値 (- \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)

極点

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

を以下に当てはめる:

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

最小値 (- \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)

極点

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

を以下に当てはめる:

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

最大値 (\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)

極点

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

を以下に当てはめる:

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

最小値 (\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)

最大値 (- \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), 最小値 (- \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), 最大値 (\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), 最小値 (\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)

グラフ

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