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Beliebt Funktionen >

extreme f(x)=x-1/6 x^2-2/3 ln(x)

Lösung

extrempunkte

f (x) = x - \frac{1}{6} x^{2} - \frac{2}{3} ln (x)

Lösung

Minimum (1, \frac{5}{6}), Maximum (2, \frac{4}{3} - \frac{2}{3} ln (2))

Schritte zur Lösung

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

Intervalle finden:

Absteigend

: 0 < x < 1,

Ansteigend

: 1 < x < 2,

Absteigend

: 2 < x < \infty

Stecke

x = 1

in

x - \frac{1}{6} x^{2} - \frac{2}{3} ln (x) : \frac{5}{6}

Minimum (1, \frac{5}{6})

Stecke

x = 2

in

x - \frac{1}{6} x^{2} - \frac{2}{3} ln (x) : \frac{4}{3} - \frac{2}{3} ln (2)

Maximum (2, \frac{4}{3} - \frac{2}{3} ln (2))

Minimum (1, \frac{5}{6}), Maximum (2, \frac{4}{3} - \frac{2}{3} ln (2))

Graph

Beliebte Beispiele

extreme y=x^3-6x^2+9x-8

e x t re m e y = x^{3} - 6 x^{2} + 9 x - 8

extreme f(x)=12+2x-x^2

e x t re m e f (x) = 12 + 2 x - x^{2}

extreme f(x)=(x^2-24)/(x-5)

e x t re m e f (x) = \frac{x ^{2} - 24}{x - 5}

extreme f(x)=ln(x)-x

e x t re m e f (x) = ln (x) - x

extreme f(x)=(4x)/(x^2+25)

e x t re m e f (x) = \frac{4 x}{x ^{2} + 25}