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Beliebt Funktionen >

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

Lösung

extrempunkte

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

Lösung

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

Schritte zur Lösung

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

Intervalle finden:

Absteigend

: - \infty < x < 0,

Ansteigend

: 0 < x < 2,

Absteigend

: 2 < x < \infty

Stecke

x = 0

in

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

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

Stecke

x = 2

in

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

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

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

Graph

Beliebte Beispiele

extreme f(x)=3+3x+x^2

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

extreme x/(ln(x)),2<= x<= 10

e x t re m e \frac{x}{ln ( x )}, 2 \leq x \leq 10

extreme f(x)=10000e^{0.17(x-1.62)^2}

e x t re m e f (x) = 10000 e^{0.17 (x - 1.62)^{2}}

extreme f(x,y)=(5x)/(1+x^2+y^2)

e x t re m e f (x, y) = \frac{5 x}{1 + x ^{2} + y ^{2}}

extreme f(x)=x^3-4x+6

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