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Beliebt Funktionen >

extreme (3x+5)/(5x^2+55x+120)

Lösung

extrempunkte

\frac{3 x + 5}{5 x ^{2} + 55 x + 120}

Lösung

Minimum (- \frac{5 + 2 19}{3}, \frac{23 + 4 19}{125}), Maximum (\frac{- 5 + 2 19}{3}, \frac{23 - 4 19}{125})

Schritte zur Lösung

f^{'} (x) = - \frac{3 x ^{2} + 10 x - 17}{5 ( x + 3 ) ^{2} ( x + 8 ) ^{2}}

Intervalle finden:

Absteigend

: - \infty < x < - 8,

Absteigend

: - 8 < x < - \frac{5 + 2 19}{3},

Ansteigend

: - \frac{5 + 2 19}{3} < x < - 3,

Ansteigend

: - 3 < x < \frac{2 19 - 5}{3},

Absteigend

: \frac{2 19 - 5}{3} < x < \infty

Stecke

x = - \frac{5 + 2 19}{3}

in

\frac{3 x + 5}{5 x ^{2} + 55 x + 120} : \frac{23 + 4 19}{125}

Minimum (- \frac{5 + 2 19}{3}, \frac{23 + 4 19}{125})

Stecke

x = \frac{- 5 + 2 19}{3}

in

\frac{3 x + 5}{5 x ^{2} + 55 x + 120} : \frac{23 - 4 19}{125}

Maximum (\frac{- 5 + 2 19}{3}, \frac{23 - 4 19}{125})

Minimum (- \frac{5 + 2 19}{3}, \frac{23 + 4 19}{125}), Maximum (\frac{- 5 + 2 19}{3}, \frac{23 - 4 19}{125})

Graph

Beliebte Beispiele

extreme f(x)=x^4e^{-7x}

e x t re m e f (x) = x^{4} e^{- 7 x}

extreme f(x)=-6x^{5/3}+\sqrt[3]{x}

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extreme y=8+2/x

e x t re m e y = 8 + \frac{2}{x}

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extreme 40x^3+9x^2-12x-8

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