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Beliebt Funktionen >

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

Lösung

extrempunkte

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

Lösung

Maximum (- \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), Minimum (- \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), Maximum (\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), Minimum (\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)

Schritte zur Lösung

Bestimme den kritischen Punkt:

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}

Bereich von

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

Intervalle finden:

Ansteigend

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

Absteigend

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

Ansteigend

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

Absteigend

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

Ansteigend

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

Setz die Extremwerte

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

in

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

ein

Maximum (- \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)

Setz die Extremwerte

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

in

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

ein

Minimum (- \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)

Setz die Extremwerte

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

in

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

ein

Maximum (\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)

Setz die Extremwerte

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

in

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

ein

Minimum (\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)

Maximum (- \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), Minimum (- \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), Maximum (\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), Minimum (\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)

Graph

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