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

Lösung

extrempunkte

f (x) = \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) = - \frac{x ^{2}}{2} + \frac{5}{2} x

e x t re m e f (x) = ln (9 - x^{2} - 9 y^{2})

e x t re m e x^{4} + y^{4} - 4 x y + 5

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

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