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Beliebt Funktionen >

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

Lösung

extrempunkte

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

Lösung

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

Schritte zur Lösung

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

Intervalle finden:

Absteigend

: - \infty < x < - 1 - 2,

Ansteigend

: - 1 - 2 < x < - 1 + 2,

Absteigend

: - 1 + 2 < x < \infty

Stecke

x = - 1 - 2

in

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

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

Stecke

x = 2 - 1

in

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

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

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

Graph

Beliebte Beispiele

extreme f(x)=x^2y+2xy-y^2-3y

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

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extreme p(b,c)=2b+2c

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extreme f(x)=|x-5|+1

e x t re m e f (x) = ∣ x - 5 ∣ + 1