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

Lösung

extrempunkte

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

Minimum (0, - 1), Maximum (2, \frac{1}{3})

Schritte zur Lösung

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

Intervalle finden:

Absteigend

: - \infty < x < 0,

Ansteigend

: 0 < x < 2,

Absteigend

: 2 < x < \infty

Stecke

x = 0

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

Minimum (0, - 1)

Stecke

x = 2

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

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

Minimum (0, - 1), Maximum (2, \frac{1}{3})

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

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

e x t re m e f (x) = (x - 10)^{\frac{1}{3}}

e x t re m e y = (2 x - 1)^{2}

e x t re m e f (x) = 3 x + \frac{147}{x}