extreme (ln(x^2))/x

Lösung

extrempunkte

\frac{ln ( x ^{2} )}{x}

Minimum (- e, - \frac{2}{e}), Maximum (e, \frac{2}{e})

Schritte zur Lösung

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

Intervalle finden:

Absteigend

: - \infty < x < - e,

Ansteigend

: - e < x < 0,

Ansteigend

: 0 < x < e,

Absteigend

: e < x < \infty

Stecke

x = - e

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

Minimum (- e, - \frac{2}{e})

Stecke

x = e

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

Maximum (e, \frac{2}{e})

Minimum (- e, - \frac{2}{e}), Maximum (e, \frac{2}{e})

e x t re m e t - 3 t

e x t re m e f (x) = 7 x x - x^{2}

e x t re m e f (x) = 3 x^{4} - 12 x^{3}

e x t re m e f (x) = x^{3} - x^{2} - 12 + 2, 0 \leq x \leq 4

e x t re m e f (x) = \frac{x ^{2}}{x ^{2} + 108}