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Beliebt Funktionen >

extreme f(x)=x^{1/3}(x-7)^2

Lösung

extrempunkte

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

Lösung

Maximum (1, 36), Minimum (7, 0)

Schritte zur Lösung

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

Intervalle finden:

Ansteigend

: - \infty < x < 0,

Ansteigend

: 0 < x < 1,

Absteigend

: 1 < x < 7,

Ansteigend

: 7 < x < \infty

Stecke

x = 1

in

x^{\frac{1}{3}} (x - 7)^{2} : 36

Maximum (1, 36)

Stecke

x = 7

in

x^{\frac{1}{3}} (x - 7)^{2} : 0

Minimum (7, 0)

Maximum (1, 36), Minimum (7, 0)

Graph

Beliebte Beispiele

extreme f(x)=4-3x-x^3

e x t re m e f (x) = 4 - 3 x - x^{3}

extreme f(x)=11-5x+x^2

e x t re m e f (x) = 11 - 5 x + x^{2}

extreme f(x)=(x^3)/3-2x^2+4

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

extreme y=(sqrt(1-x^2))/x

e x t re m e y = \frac{1 - x ^{2}}{x}

extreme F(X,Y)=2X+3YX^2

e x t re m e F (X, Y) = 2 X + 3 Y X^{2}