extreme f(x)=((ln(x))^2)/x

Lösung

extrempunkte

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

Minimum (1, 0), Maximum (e^{2}, \frac{4}{e ^{2}})

Schritte zur Lösung

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

Intervalle finden:

Absteigend

: 0 < x < 1,

Ansteigend

: 1 < x < e^{2},

Absteigend

: e^{2} < x < \infty

Stecke

x = 1

\frac{ln ^{2} ( x )}{x} : 0

Minimum (1, 0)

Stecke

x = e^{2}

\frac{ln ^{2} ( x )}{x} : \frac{4}{e ^{2}}

Maximum (e^{2}, \frac{4}{e ^{2}})

Minimum (1, 0), Maximum (e^{2}, \frac{4}{e ^{2}})

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

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

e x t re m e f (x) = 6 x^{2} + 6 y^{2} + 6 x y + 36 x - 54 y - 5

e x t re m e K (r, s) = 9 r - s

e x t re m e f (x, y) = ln (2 - x^{2} - y^{2})