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Beliebt Funktionen >

extreme y=x^{2/7}(x^2-4)

Lösung

extrempunkte

y = x^{\frac{2}{7}} (x^{2} - 4)

Lösung

Minimum - \frac{1}{2 ^{\frac{1}{2}}}, - \frac{7 ( - \frac{1}{2 ^{\frac{1}{2}}} ) ^{\frac{2}{7}}}{2}, Maximum (0, 0), Minimum (\frac{1}{2 ^{\frac{1}{2}}}, - \frac{7}{2 \cdot 2 ^{\frac{1}{7}}})

Schritte zur Lösung

f^{'} (x) = \frac{8 ( 2 ^{\frac{1}{2}} x + 1 ) ( 2 ^{\frac{1}{2}} x - 1 )}{7 x ^{\frac{5}{7}}}

Intervalle finden:

Absteigend

: - \infty < x < - \frac{1}{2 ^{\frac{1}{2}}},

Ansteigend

: - \frac{1}{2 ^{\frac{1}{2}}} < x < 0,

Absteigend

: 0 < x < \frac{1}{2 ^{\frac{1}{2}}},

Ansteigend

: \frac{1}{2 ^{\frac{1}{2}}} < x < \infty

Stecke

x = - \frac{1}{2 ^{\frac{1}{2}}}

in

x^{\frac{2}{7}} (x^{2} - 4) : - \frac{7 ( - \frac{1}{2 ^{\frac{1}{2}}} ) ^{\frac{2}{7}}}{2}

Minimum - \frac{1}{2 ^{\frac{1}{2}}}, - \frac{7 ( - \frac{1}{2 ^{\frac{1}{2}}} ) ^{\frac{2}{7}}}{2}

Stecke

x = 0

in

x^{\frac{2}{7}} (x^{2} - 4) : 0

Maximum (0, 0)

Stecke

x = \frac{1}{2 ^{\frac{1}{2}}}

in

x^{\frac{2}{7}} (x^{2} - 4) : - \frac{7}{2 \cdot 2 ^{\frac{1}{7}}}

Minimum (\frac{1}{2 ^{\frac{1}{2}}}, - \frac{7}{2 \cdot 2 ^{\frac{1}{7}}})

Minimum - \frac{1}{2 ^{\frac{1}{2}}}, - \frac{7 ( - \frac{1}{2 ^{\frac{1}{2}}} ) ^{\frac{2}{7}}}{2}, Maximum (0, 0), Minimum (\frac{1}{2 ^{\frac{1}{2}}}, - \frac{7}{2 \cdot 2 ^{\frac{1}{7}}})

Graph

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