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Beliebt Funktionen >

inflection (ln(x))/x

Lösung

wendepunkte

\frac{ln ( x )}{x}

Lösung

(e^{\frac{3}{2}}, \frac{3}{2 e ^{\frac{3}{2}}})

Schritte zur Lösung

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

Intervalle finden:

Konkav fallend

: 0 < x < e^{\frac{3}{2}},

Konkav steigend

: e^{\frac{3}{2}} < x < \infty

Stecke

x = e^{\frac{3}{2}}

in

\frac{ln ( x )}{x} : \frac{3}{2 e ^{\frac{3}{2}}}

(e^{\frac{3}{2}}, \frac{3}{2 e ^{\frac{3}{2}}})

Graph

Beliebte Beispiele

monotone (x^2+2x-1)(2x^2-3x+6)

m o n o t o n e (x^{2} + 2 x - 1) (2 x^{2} - 3 x + 6)

extreme f(x)=4-x^2

e x t re m e f (x) = 4 - x^{2}

domäne f(x)=5x-10

d o main f (x) = 5 x - 10

invers y=x^2-4x

in v erse y = x^{2} - 4 x

asymptoten f(x)=(x^4-16)/(2x^2-4x)

a sy m pt o t es f (x) = \frac{x ^{4} - 16}{2 x ^{2} - 4 x}