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Beliebt Funktionen >

extreme f(x)=x*(ln(x))^5

Lösung

extrempunkte

f (x) = x \cdot (ln (x))^{5}

Lösung

Minimum (\frac{1}{e ^{5}}, - \frac{3125}{e ^{5}}), Sattel (1, 0)

Schritte zur Lösung

f^{'} (x) = ln^{5} (x) + 5 ln^{4} (x)

Intervalle finden:

Absteigend

: 0 < x < \frac{1}{e ^{5}},

Ansteigend

: \frac{1}{e ^{5}} < x < 1,

Ansteigend

: 1 < x < \infty

Stecke

x = \frac{1}{e ^{5}}

in

x \cdot ln^{5} (x) : - \frac{3125}{e ^{5}}

Minimum (\frac{1}{e ^{5}}, - \frac{3125}{e ^{5}})

Stecke

x = 1

in

x \cdot ln^{5} (x) : 0

Sattel (1, 0)

Minimum (\frac{1}{e ^{5}}, - \frac{3125}{e ^{5}}), Sattel (1, 0)

Graph

Beliebte Beispiele

extreme f(x,y)=40000x+30000y-8x^2-15y^2-10xy

e x t re m e f (x, y) = 40000 x + 30000 y - 8 x^{2} - 15 y^{2} - 10 x y

extreme f(x)=e^{x^3-3x}

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

extreme f(x)=x+(30)/x

e x t re m e f (x) = x + \frac{30}{x}

extreme (5x+4)/(x+sqrt(x))

e x t re m e \frac{5 x + 4}{x + x}

extreme F(x,y)=x*y+(pi*(x/2)^2)/2

e x t re m e F (x, y) = x \cdot y + \frac{π \cdot ( \frac{x}{2} ) ^{2}}{2}