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Beliebt Funktionen >

extreme 8/x+2pix^2

Lösung

extrempunkte

\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)=8x 5/6 y 1/6

e x t re m e f (x, y) = 8 x \frac{5}{6} y \frac{1}{6}

extreme f(x,y)=x^3y+3x^2y^2+2y^2+2

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

extreme f(x)=e^{x-[x]}

e x t re m e f (x) = e^{x - [x]}

extreme f(x)=x(18-48+2x)(48/2-x)

e x t re m e f (x) = x (18 - 48 + 2 x) (\frac{48}{2} - x)

extreme f(x)=(5e^{4x})/(2x-5)

e x t re m e f (x) = \frac{5 e ^{4 x}}{2 x - 5}