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Beliebt Funktionen >

extreme f(x)=x^3e^{(4-2x^2)}

Lösung

extrempunkte

f (x) = x^{3} e^{(4 - 2 x^{2})}

Lösung

Minimum (- \frac{3}{2}, - \frac{3 3 e ^{\frac{5}{2}}}{8}), Sattel (0, 0), Maximum (\frac{3}{2}, \frac{3 3 e ^{\frac{5}{2}}}{8})

Schritte zur Lösung

f^{'} (x) = - e^{- 2 (2 + x) (- 2 + x)} x^{2} (2 x + 3) (2 x - 3)

Intervalle finden:

Absteigend

: - \infty < x < - \frac{3}{2},

Ansteigend

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

Ansteigend

: 0 < x < \frac{3}{2},

Absteigend

: \frac{3}{2} < x < \infty

Stecke

x = - \frac{3}{2}

in

x^{3} e^{4 - 2 x^{2}} : - \frac{3 3 e ^{\frac{5}{2}}}{8}

Minimum (- \frac{3}{2}, - \frac{3 3 e ^{\frac{5}{2}}}{8})

Stecke

x = 0

in

x^{3} e^{4 - 2 x^{2}} : 0

Sattel (0, 0)

Stecke

x = \frac{3}{2}

in

x^{3} e^{4 - 2 x^{2}} : \frac{3 3 e ^{\frac{5}{2}}}{8}

Maximum (\frac{3}{2}, \frac{3 3 e ^{\frac{5}{2}}}{8})

Minimum (- \frac{3}{2}, - \frac{3 3 e ^{\frac{5}{2}}}{8}), Sattel (0, 0), Maximum (\frac{3}{2}, \frac{3 3 e ^{\frac{5}{2}}}{8})

Graph

Beliebte Beispiele

e x t re m e 22 x^{2}

extreme f(x)=(e^x)/(x^3),x>0

e x t re m e f (x) = \frac{e ^{x}}{x ^{3}}, x > 0

extreme 36xy-x^3-8y^3

e x t re m e 36 x y - x^{3} - 8 y^{3}

extreme f(x)=\sqrt[5]{x},-1<= x<= 0

e x t re m e f (x) = 5 x, - 1 \leq x \leq 0

extreme (20)/r+5pir^2

e x t re m e \frac{20}{r} + 5 π r^{2}