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Beliebt Funktionen >

extreme x^5-x^3

Lösung

extrempunkte

x^{5} - x^{3}

Lösung

Maximum (- \frac{3}{5}, - (\frac{3}{5})^{\frac{5}{2}} + (\frac{3}{5})^{\frac{3}{2}}), Sattel (0, 0), Minimum (\frac{3}{5}, (\frac{3}{5})^{\frac{5}{2}} - (\frac{3}{5})^{\frac{3}{2}})

Schritte zur Lösung

f^{'} (x) = 5 x^{4} - 3 x^{2}

Intervalle finden:

Ansteigend

: - \infty < x < - \frac{3}{5},

Absteigend

: - \frac{3}{5} < x < 0,

Absteigend

: 0 < x < \frac{3}{5},

Ansteigend

: \frac{3}{5} < x < \infty

Stecke

x = - \frac{3}{5}

in

x^{5} - x^{3} : - (\frac{3}{5})^{\frac{5}{2}} + (\frac{3}{5})^{\frac{3}{2}}

Maximum (- \frac{3}{5}, - (\frac{3}{5})^{\frac{5}{2}} + (\frac{3}{5})^{\frac{3}{2}})

Stecke

x = 0

in

x^{5} - x^{3} : 0

Sattel (0, 0)

Stecke

x = \frac{3}{5}

in

x^{5} - x^{3} : (\frac{3}{5})^{\frac{5}{2}} - (\frac{3}{5})^{\frac{3}{2}}

Minimum (\frac{3}{5}, (\frac{3}{5})^{\frac{5}{2}} - (\frac{3}{5})^{\frac{3}{2}})

Maximum (- \frac{3}{5}, - (\frac{3}{5})^{\frac{5}{2}} + (\frac{3}{5})^{\frac{3}{2}}), Sattel (0, 0), Minimum (\frac{3}{5}, (\frac{3}{5})^{\frac{5}{2}} - (\frac{3}{5})^{\frac{3}{2}})

Graph

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