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Beliebt Funktionen >

extreme 1/(x^3-2x)

Lösung

extrempunkte

\frac{1}{x ^{3} - 2 x}

Lösung

Minimum - \frac{2}{3}, \frac{27 ( ( \frac{2}{3} ) ^{\frac{3}{2}} + 2 \frac{2}{3} )}{64}, Maximum \frac{2}{3}, - \frac{27 ( ( \frac{2}{3} ) ^{\frac{3}{2}} + 2 \frac{2}{3} )}{64}

Schritte zur Lösung

f^{'} (x) = - \frac{3 x ^{2} - 2}{( x ^{3} - 2 x ) ^{2}}

Intervalle finden:

Absteigend

: - \infty < x < - 2,

Absteigend

: - 2 < x < - \frac{2}{3},

Ansteigend

: - \frac{2}{3} < x < 0,

Ansteigend

: 0 < x < \frac{2}{3},

Absteigend

: \frac{2}{3} < x < 2,

Absteigend

: 2 < x < \infty

Stecke

x = - \frac{2}{3}

in

\frac{1}{x ^{3} - 2 x} : \frac{27 ( ( \frac{2}{3} ) ^{\frac{3}{2}} + 2 \frac{2}{3} )}{64}

Minimum - \frac{2}{3}, \frac{27 ( ( \frac{2}{3} ) ^{\frac{3}{2}} + 2 \frac{2}{3} )}{64}

Stecke

x = \frac{2}{3}

in

\frac{1}{x ^{3} - 2 x} : - \frac{27 ( ( \frac{2}{3} ) ^{\frac{3}{2}} + 2 \frac{2}{3} )}{64}

Maximum \frac{2}{3}, - \frac{27 ( ( \frac{2}{3} ) ^{\frac{3}{2}} + 2 \frac{2}{3} )}{64}

Minimum - \frac{2}{3}, \frac{27 ( ( \frac{2}{3} ) ^{\frac{3}{2}} + 2 \frac{2}{3} )}{64}, Maximum \frac{2}{3}, - \frac{27 ( ( \frac{2}{3} ) ^{\frac{3}{2}} + 2 \frac{2}{3} )}{64}

Graph

Beliebte Beispiele

extreme f(x,y)=4y^3x^2-12y^2-36y+2

e x t re m e f (x, y) = 4 y^{3} x^{2} - 12 y^{2} - 36 y + 2

extreme f(x)=-2x^3+39x^2-240,4<= x<= 9

e x t re m e f (x) = - 2 x^{3} + 39 x^{2} - 240, 4 \leq x \leq 9

extreme f(x)=8(x^2)/((x-6)),-3<= x<= 2

e x t re m e f (x) = 8 \frac{x ^{2}}{( x - 6 )}, - 3 \leq x \leq 2

extreme f(x)=-0.05x^2+300x+2000

e x t re m e f (x) = - 0.05 x^{2} + 300 x + 2000

extreme f(x,y)=e^{x^2}+y^2+1

e x t re m e f (x, y) = e^{x^{2}} + y^{2} + 1