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Beliebt Funktionen >

extreme f(x)=(12)/x+3pix^2

Lösung

extrempunkte

f (x) = \frac{12}{x} + 3 π x^{2}

Lösung

Minimum (3 \frac{2}{π}, 6 \cdot 2^{\frac{2}{3}} 3 π + 3 π (\frac{2}{π})^{\frac{2}{3}})

Schritte zur Lösung

f^{'} (x) = - \frac{12}{x ^{2}} + 6 π x

Intervalle finden:

Absteigend

: - \infty < x < 0,

Absteigend

: 0 < x < \frac{3 4}{3 2 3 π},

Ansteigend

: \frac{3 4}{3 2 3 π} < x < \infty

Stecke

x = 3 \frac{2}{π}

in

\frac{12}{x} + 3 π x^{2} : 6 \cdot 2^{\frac{2}{3}} 3 π + 3 π (\frac{2}{π})^{\frac{2}{3}}

Minimum (3 \frac{2}{π}, 6 \cdot 2^{\frac{2}{3}} 3 π + 3 π (\frac{2}{π})^{\frac{2}{3}})

Graph

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