extreme (sqrt(x))/(1+x)

Lösung

extrempunkte

\frac{x}{1 + x}

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

Schritte zur Lösung

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

Intervalle finden:

Ansteigend

: 0 < x < 1,

Absteigend

: 1 < x < \infty

Stecke

x = 0

\frac{x}{1 + x} : 0

Minimum (0, 0)

Stecke

x = 1

\frac{x}{1 + x} : \frac{1}{2}

Maximum (1, \frac{1}{2})

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

e x t re m e f (x) = x^{3} - 6 x^{2} + 4

e x t re m e f (x) = \frac{x ^{2} - x - 2}{x ^{2} - 6 x + 9}

e x t re m e f (x, y) = x y + \frac{8}{x} + \frac{8}{y}

e x t re m e f (x, y) = x y - 5 x - 5 y - x^{2} - y^{2}

e x t re m e f (x, y) = - 5 x^{2} + 4 x y - y^{2} + 16 x + 10