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

Lösung

extrempunkte

y = \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, y) = - x^{3} + 2 y^{3} + 27 x - 24 y + 3

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

e x t re m e F (I, J) = (- 3 I + 2 J)

e x t re m e 0.5 x^{2} - 130 x + 17555

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