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Beliebt Funktionen >

extreme f(x)=(((x^2-1)^{0.5})/(x^3))

Lösung

extrempunkte

f (x) = (\frac{( x ^{2} - 1 ) ^{0.5}}{x ^{3}})

Lösung

Minimum (- \frac{3}{2}, - \frac{2}{3 \cdot 3 ^{\frac{1}{2}}}), Maximum (- 1, 0), Minimum (1, 0), Maximum (\frac{3}{2}, \frac{2}{3 \cdot 3 ^{\frac{1}{2}}})

Schritte zur Lösung

f^{'} (x) = \frac{- 2 x ^{2} + 3}{x ^{4} ( x ^{2} - 1 ) ^{\frac{1}{2}}}

Intervalle finden:

Absteigend

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

Ansteigend

: - \frac{3}{2} < x < - 1,

Ansteigend

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

Absteigend

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

Stecke

x = - \frac{3}{2}

in

\frac{( x ^{2} - 1 ) ^{0.5}}{x ^{3}} : - \frac{2}{3 \cdot 3 ^{\frac{1}{2}}}

Minimum (- \frac{3}{2}, - \frac{2}{3 \cdot 3 ^{\frac{1}{2}}})

Stecke

x = - 1

in

\frac{( x ^{2} - 1 ) ^{0.5}}{x ^{3}} : 0

Maximum (- 1, 0)

Stecke

x = 1

in

\frac{( x ^{2} - 1 ) ^{0.5}}{x ^{3}} : 0

Minimum (1, 0)

Stecke

x = \frac{3}{2}

in

\frac{( x ^{2} - 1 ) ^{0.5}}{x ^{3}} : \frac{2}{3 \cdot 3 ^{\frac{1}{2}}}

Maximum (\frac{3}{2}, \frac{2}{3 \cdot 3 ^{\frac{1}{2}}})

Minimum (- \frac{3}{2}, - \frac{2}{3 \cdot 3 ^{\frac{1}{2}}}), Maximum (- 1, 0), Minimum (1, 0), Maximum (\frac{3}{2}, \frac{2}{3 \cdot 3 ^{\frac{1}{2}}})

Graph

Beliebte Beispiele

extreme f(x,y)=6x^2+9xy+3y^2+8xy^2+5x^2y

e x t re m e f (x, y) = 6 x^{2} + 9 x y + 3 y^{2} + 8 x y^{2} + 5 x^{2} y

extreme (x^2-11)/(x-6)

e x t re m e \frac{x ^{2} - 11}{x - 6}

extreme f(x,y)=(2xy)/((2x+3y-4))

e x t re m e f (x, y) = \frac{2 x y}{( 2 x + 3 y - 4 )}

extreme f(x)=-2x+3ln(4x),(1,5)

e x t re m e f (x) = - 2 x + 3 ln (4 x), (1, 5)

extreme f(x)=x^3+3x^2-9

e x t re m e f (x) = x^{3} + 3 x^{2} - 9