extreme (x^2+x)/(x-1)

Lösung

extrempunkte

\frac{x ^{2} + x}{x - 1}

Maximum (1 - 2, \frac{3 2 - 4}{2}), Minimum (1 + 2, \frac{4 + 3 2}{2})

Schritte zur Lösung

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

Intervalle finden:

Ansteigend

: - \infty < x < 1 - 2,

Absteigend

: 1 - 2 < x < 1,

Absteigend

: 1 < x < 1 + 2,

Ansteigend

: 1 + 2 < x < \infty

Stecke

x = 1 - 2

\frac{x ^{2} + x}{x - 1} : \frac{3 2 - 4}{2}

Maximum (1 - 2, \frac{3 2 - 4}{2})

Stecke

x = 1 + 2

\frac{x ^{2} + x}{x - 1} : \frac{4 + 3 2}{2}

Minimum (1 + 2, \frac{4 + 3 2}{2})

Maximum (1 - 2, \frac{3 2 - 4}{2}), Minimum (1 + 2, \frac{4 + 3 2}{2})

e x t re m e \frac{ln ( x )}{6 x}

e x t re m e h (x) = - 6 x^{3} + 18 x^{2} + 3

e x t re m e F (x) = \frac{2 x}{x ^{2} + 16}, - 8 \leq x \leq 8

e x t re m e - (\frac{9}{2})^{2} - 7^{2} + \frac{9}{2} - 14 + 3

e x t re m e x (8 - x^{2})