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Beliebt Funktionen >

extreme f(x)=(1/x)+2+(4/(1-x))

Lösung

extrempunkte

f (x) = (\frac{1}{x}) + 2 + (\frac{4}{1 - x})

Lösung

Maximum (- 1, 3), Minimum (\frac{1}{3}, 11)

Schritte zur Lösung

f^{'} (x) = \frac{( x + 1 ) ( 3 x - 1 )}{x ^{2} ( - x + 1 ) ^{2}}

Intervalle finden:

Ansteigend

: - \infty < x < - 1,

Absteigend

: - 1 < x < 0,

Absteigend

: 0 < x < \frac{1}{3},

Ansteigend

: \frac{1}{3} < x < 1,

Ansteigend

: 1 < x < \infty

Stecke

x = - 1

in

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

Maximum (- 1, 3)

Stecke

x = \frac{1}{3}

in

\frac{1}{x} + 2 + \frac{4}{1 - x} : 11

Minimum (\frac{1}{3}, 11)

Maximum (- 1, 3), Minimum (\frac{1}{3}, 11)

Graph

Beliebte Beispiele

extreme f(x)=2x^3-x^2-20x+10

e x t re m e f (x) = 2 x^{3} - x^{2} - 20 x + 10

extreme f(x)=x^3*e^{-2x^2}

e x t re m e f (x) = x^{3} \cdot e^{- 2 x^{2}}

extreme f(x,y)=x^2+5xy+y^2-2x+y-6

e x t re m e f (x, y) = x^{2} + 5 x y + y^{2} - 2 x + y - 6

extreme f(x)=2x^3+3x^2-9x-9

e x t re m e f (x) = 2 x^{3} + 3 x^{2} - 9 x - 9

extreme f(x)= 1/4 x^4-x,-4<= x<= 4

e x t re m e f (x) = \frac{1}{4} x^{4} - x, - 4 \leq x \leq 4