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Beliebt Funktionen >

extreme f(x)=x^2log_{8}(x)

Lösung

extrempunkte

f (x) = x^{2} lo g_{8} (x)

Lösung

Minimum \frac{1}{8 ^{\frac{1}{6 l n ( 2 )}}}, \frac{lo g _{8} ( \frac{1}{8 ^{\frac{1}{6 l n ( 2 )}}} )}{8 ^{\frac{1}{3 l n ( 2 )}}}

Schritte zur Lösung

f^{'} (x) = 2 x lo g_{8} (x) + \frac{x}{3 ln ( 2 )}

Intervalle finden:

Absteigend

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

Ansteigend

: \frac{1}{e} < x < \infty

Stecke

x = \frac{1}{8 ^{\frac{1}{6 l n ( 2 )}}}

in

x^{2} lo g_{8} (x) : \frac{lo g _{8} ( \frac{1}{8 ^{\frac{1}{6 l n ( 2 )}}} )}{8 ^{\frac{1}{3 l n ( 2 )}}}

Minimum \frac{1}{8 ^{\frac{1}{6 l n ( 2 )}}}, \frac{lo g _{8} ( \frac{1}{8 ^{\frac{1}{6 l n ( 2 )}}} )}{8 ^{\frac{1}{3 l n ( 2 )}}}

Graph

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