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Beliebt Funktionen >

extreme f(x)=2pir^2+(1500)/r

Lösung

extrempunkte

f (x) = 2 π r^{2} + \frac{1500}{r}

Lösung

Minimum (\frac{5 3 3}{3 π}, 50 \cdot 3^{\frac{2}{3}} π^{\frac{1}{3}} + 100 \cdot 3^{\frac{2}{3}} 3 π)

Schritte zur Lösung

f^{'} (r) = 4 π r - \frac{1500}{r ^{2}}

Intervalle finden:

Absteigend

: - \infty < r < 0,

Absteigend

: 0 < r < \frac{5 3 3}{3 π},

Ansteigend

: \frac{5 3 3}{3 π} < r < \infty

Stecke

r = \frac{5 3 3}{3 π}

in

2 π r^{2} + \frac{1500}{r} : 50 \cdot 3^{\frac{2}{3}} π^{\frac{1}{3}} + 100 \cdot 3^{\frac{2}{3}} 3 π

Minimum (\frac{5 3 3}{3 π}, 50 \cdot 3^{\frac{2}{3}} π^{\frac{1}{3}} + 100 \cdot 3^{\frac{2}{3}} 3 π)

Graph

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