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Beliebt Funktionen >

extreme sqrt(x-2)e^{-x/2}

Lösung

extrempunkte

x - 2 e^{- \frac{x}{2}}

Lösung

Minimum (2, 0), Maximum (3, \frac{1}{e ^{\frac{3}{2}}})

Schritte zur Lösung

f^{'} (x) = \frac{e ^{- \frac{x}{2}}}{2 ( x - 2 ) ^{\frac{1}{2}}} - \frac{e ^{- \frac{x}{2}} x - 2}{2}

Intervalle finden:

Ansteigend

: 2 < x < 3,

Absteigend

: 3 < x < \infty

Stecke

x = 2

in

x - 2 e^{- \frac{x}{2}} : 0

Minimum (2, 0)

Stecke

x = 3

in

x - 2 e^{- \frac{x}{2}} : \frac{1}{e ^{\frac{3}{2}}}

Maximum (3, \frac{1}{e ^{\frac{3}{2}}})

Minimum (2, 0), Maximum (3, \frac{1}{e ^{\frac{3}{2}}})

Graph

Beliebte Beispiele

extreme f(x,y)=x^3-3xy+1/2 y^2

e x t re m e f (x, y) = x^{3} - 3 x y + \frac{1}{2} y^{2}

extreme f(x)=(x+2)/(x^2-x-6)

e x t re m e f (x) = \frac{x + 2}{x ^{2} - x - 6}

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

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

extreme f(x)=7+3x+x^2

e x t re m e f (x) = 7 + 3 x + x^{2}

extreme-0.25x^2+40x+300

e x t re m e - 0.25 x^{2} + 40 x + 300