de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Funktionen >

extreme f(x)=(-2x^2+14x-24)/(x^2+2x)

Lösung

extrempunkte

f (x) = \frac{- 2 x ^{2} + 14 x - 24}{x ^{2} + 2 x}

Lösung

Minimum (- \frac{2 ( 10 - 2 )}{3}, 610 + 19), Maximum (\frac{2 ( 2 + 10 )}{3}, 19 - 610)

Schritte zur Lösung

f^{'} (x) = \frac{- 18 x ^{2} + 48 x + 48}{( x ^{2} + 2 x ) ^{2}}

Intervalle finden:

Absteigend

: - \infty < x < - 2,

Absteigend

: - 2 < x < \frac{2 ( 2 - 10 )}{3},

Ansteigend

: \frac{2 ( 2 - 10 )}{3} < x < 0,

Ansteigend

: 0 < x < \frac{2 ( 2 + 10 )}{3},

Absteigend

: \frac{2 ( 2 + 10 )}{3} < x < \infty

Stecke

x = - \frac{2 ( 10 - 2 )}{3}

in

\frac{- 2 x ^{2} + 14 x - 24}{x ^{2} + 2 x} : 610 + 19

Minimum (- \frac{2 ( 10 - 2 )}{3}, 610 + 19)

Stecke

x = \frac{2 ( 2 + 10 )}{3}

in

\frac{- 2 x ^{2} + 14 x - 24}{x ^{2} + 2 x} : 19 - 610

Maximum (\frac{2 ( 2 + 10 )}{3}, 19 - 610)

Minimum (- \frac{2 ( 10 - 2 )}{3}, 610 + 19), Maximum (\frac{2 ( 2 + 10 )}{3}, 19 - 610)

Graph

Beliebte Beispiele

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

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

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

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

extreme f(x)=3x^{5/3}-2x^{2/3}

e x t re m e f (x) = 3 x^{\frac{5}{3}} - 2 x^{\frac{2}{3}}

extreme g(x)=-x^3+3x-10

e x t re m e g (x) = - x^{3} + 3 x - 10

extreme f(x)=(x^4-5x+7)/(x^2+1)

e x t re m e f (x) = \frac{x ^{4} - 5 x + 7}{x ^{2} + 1}