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Beliebt Funktionen >

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

Lösung

extrempunkte

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

Lösung

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

Schritte zur Lösung

f^{'} (x) = - e^{- 2 x^{2}} 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} \cdot e^{- 2 x^{2}} : - \frac{3 3}{8 e ^{\frac{3}{2}}}

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

Stecke

x = 0

in

x^{3} \cdot e^{- 2 x^{2}} : 0

Sattel (0, 0)

Stecke

x = \frac{3}{2}

in

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

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

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

Graph

Beliebte Beispiele

extreme f(x,y)=x^2+5xy+y^2-2x+y-6

e x t re m e f (x, y) = x^{2} + 5 x y + y^{2} - 2 x + y - 6

extreme f(x)=2x^3+3x^2-9x-9

e x t re m e f (x) = 2 x^{3} + 3 x^{2} - 9 x - 9

extreme f(x)= 1/4 x^4-x,-4<= x<= 4

e x t re m e f (x) = \frac{1}{4} x^{4} - x, - 4 \leq x \leq 4

e x t re m e 12

extreme f(x)=(x^2+10)(100-x^2)

e x t re m e f (x) = (x^{2} + 10) (100 - x^{2})