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Beliebt Funktionen >

extreme f(x)=(x^2+2)/(x^2-4x)

Lösung

extrempunkte

f (x) = \frac{x ^{2} + 2}{x ^{2} - 4 x}

Lösung

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

Schritte zur Lösung

f^{'} (x) = \frac{- 4 x ^{2} - 4 x + 8}{( x ^{2} - 4 x ) ^{2}}

Intervalle finden:

Absteigend

: - \infty < x < - 2,

Ansteigend

: - 2 < x < 0,

Ansteigend

: 0 < x < 1,

Absteigend

: 1 < x < 4,

Absteigend

: 4 < x < \infty

Stecke

x = - 2

in

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

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

Stecke

x = 1

in

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

Maximum (1, - 1)

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

Graph

Beliebte Beispiele

extreme f(x)=x^7ln(x)

e x t re m e f (x) = x^{7} ln (x)

extreme f(x)= 1/3 x^3+11/2 x^2+24x+1

e x t re m e f (x) = \frac{1}{3} x^{3} + \frac{11}{2} x^{2} + 24 x + 1

extreme f(x)=x^4(x+2)^2

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

extreme f(x)=(x+3)/(x^2-4x-21)

e x t re m e f (x) = \frac{x + 3}{x ^{2} - 4 x - 21}

extreme f(x)=5xsqrt(x-x^2)

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