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Beliebt Funktionen >

extreme f(x)= 6/7 (x^2-9)^{2/3}

Lösung

extrempunkte

f (x) = \frac{6}{7} (x^{2} - 9)^{\frac{2}{3}}

Lösung

Minimum (- 3, 0), Maximum (0, \frac{6 ( - 9 ) ^{\frac{2}{3}}}{7}), Minimum (3, 0)

Schritte zur Lösung

f^{'} (x) = \frac{8 x}{7 ( x ^{2} - 9 ) ^{\frac{1}{3}}}

Intervalle finden:

Absteigend

: - \infty < x < - 3,

Ansteigend

: - 3 < x < 0,

Absteigend

: 0 < x < 3,

Ansteigend

: 3 < x < \infty

Stecke

x = - 3

in

\frac{6}{7} (x^{2} - 9)^{\frac{2}{3}} : 0

Minimum (- 3, 0)

Stecke

x = 0

in

\frac{6}{7} (x^{2} - 9)^{\frac{2}{3}} : \frac{6 ( - 9 ) ^{\frac{2}{3}}}{7}

Maximum (0, \frac{6 ( - 9 ) ^{\frac{2}{3}}}{7})

Stecke

x = 3

in

\frac{6}{7} (x^{2} - 9)^{\frac{2}{3}} : 0

Minimum (3, 0)

Minimum (- 3, 0), Maximum (0, \frac{6 ( - 9 ) ^{\frac{2}{3}}}{7}), Minimum (3, 0)

Graph

Beliebte Beispiele

extreme f(x,y)=7xy+14x-x^2+2y^2

e x t re m e f (x, y) = 7 x y + 14 x - x^{2} + 2 y^{2}

extreme 4x^2-8x^4

e x t re m e 4 x^{2} - 8 x^{4}

extreme f(x)=(x^2(x-1))/(x+2),x\ne 2

e x t re m e f (x) = \frac{x ^{2} ( x - 1 )}{x + 2}, x \neq = 2

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e x t re m e f (x) = 9 x^{3} + 21 x^{2} + 8 x - 3

extreme f(x)=x^2-2x+5[-1.4]

e x t re m e f (x) = x^{2} - 2 x + 5 [- 1.4]