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Beliebt Funktionen >

extreme e^x(2x^2+x-8)

Lösung

extrempunkte

e^{x} (2 x^{2} + x - 8)

Lösung

Maximum (- \frac{7}{2}, \frac{13}{e ^{\frac{7}{2}}}), Minimum (1, - 5 e)

Schritte zur Lösung

f^{'} (x) = e^{x} (x - 1) (2 x + 7)

Intervalle finden:

Ansteigend

: - \infty < x < - \frac{7}{2},

Absteigend

: - \frac{7}{2} < x < 1,

Ansteigend

: 1 < x < \infty

Stecke

x = - \frac{7}{2}

in

e^{x} (2 x^{2} + x - 8) : \frac{13}{e ^{\frac{7}{2}}}

Maximum (- \frac{7}{2}, \frac{13}{e ^{\frac{7}{2}}})

Stecke

x = 1

in

e^{x} (2 x^{2} + x - 8) : - 5 e

Minimum (1, - 5 e)

Maximum (- \frac{7}{2}, \frac{13}{e ^{\frac{7}{2}}}), Minimum (1, - 5 e)

Graph

Beliebte Beispiele

extreme f(x)=2x^3+18x^2+54x+50

e x t re m e f (x) = 2 x^{3} + 18 x^{2} + 54 x + 50

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

extreme x^3+6x^2-63x+10

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