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Beliebt Funktionen >

extreme f(x)= 8/x+2pix^2

Lösung

extrempunkte

f (x) = \frac{8}{x} + 2 π x^{2}

Lösung

Minimum (3 \frac{2}{π}, 4 \cdot 2^{\frac{2}{3}} 3 π + 2 π (\frac{2}{π})^{\frac{2}{3}})

Schritte zur Lösung

f^{'} (x) = - \frac{8}{x ^{2}} + 4 π x

Intervalle finden:

Absteigend

: - \infty < x < 0,

Absteigend

: 0 < x < \frac{2}{3 4 3 π},

Ansteigend

: \frac{2}{3 4 3 π} < x < \infty

Stecke

x = 3 \frac{2}{π}

in

\frac{8}{x} + 2 π x^{2} : 4 \cdot 2^{\frac{2}{3}} 3 π + 2 π (\frac{2}{π})^{\frac{2}{3}}

Minimum (3 \frac{2}{π}, 4 \cdot 2^{\frac{2}{3}} 3 π + 2 π (\frac{2}{π})^{\frac{2}{3}})

Graph

Beliebte Beispiele

extreme f(x,y)=sqrt(400-9x^2-36y^2)

e x t re m e f (x, y) = 400 - 9 x^{2} - 36 y^{2}

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

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

extreme f(x,y)=4-x^4+2x^2-y^2

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

extreme f(x)=(x^2-1)^3,-1<= x<= 6

e x t re m e f (x) = (x^{2} - 1)^{3}, - 1 \leq x \leq 6

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

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