extreme f(x)=(ln(5x))/x

Lösung

extrempunkte

f (x) = \frac{ln ( 5 x )}{x}

Maximum (\frac{e}{5}, \frac{5}{e})

Schritte zur Lösung

f^{'} (x) = \frac{1 - ln ( 5 x )}{x ^{2}}

Intervalle finden:

Ansteigend

: 0 < x < \frac{e}{5},

Absteigend

: \frac{e}{5} < x < \infty

Stecke

x = \frac{e}{5}

\frac{ln ( 5 x )}{x} : \frac{5}{e}

Maximum (\frac{e}{5}, \frac{5}{e})

e x t re m e f (x, y) = x^{2} - 4 x - y^{2} - 6 y + 7

e x t re m e f (x) = x^{5} - 5 x^{4} + 5 = x^{4} (x - 5) + 5

e x t re m e f (x, y) = 2 x y - x^{2} - 6 y^{2} + 4 x + 1

e x t re m e f (x) = - x^{2} - 2 x + 99

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