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Beliebt Funktionen >

extreme-8x^{5/3}+\sqrt[3]{x}

Lösung

extrempunkte

- 8 x^{\frac{5}{3}} + 3 x

Lösung

Minimum (- \frac{1}{1 0 ^{\frac{1}{4}} \cdot 4 5}, - 8 (- \frac{1}{4 \cdot 1 0 ^{\frac{1}{4}} 5})^{\frac{5}{3}} - (\frac{1}{4 \cdot 1 0 ^{\frac{1}{4}} 5})^{\frac{1}{3}}), Maximum (\frac{1}{1 0 ^{\frac{1}{4}} \cdot 4 5}, - 8 (\frac{1}{1 0 ^{\frac{1}{4}} \cdot 4 5})^{\frac{5}{3}} + 3 \frac{1}{1 0 ^{\frac{1}{4}} \cdot 4 5})

Schritte zur Lösung

f^{'} (x) = - \frac{40 x ^{\frac{2}{3}}}{3} + \frac{1}{3 x ^{\frac{2}{3}}}

Intervalle finden:

Absteigend

: - \infty < x < - \frac{1}{4 0 ^{\frac{3}{4}}},

Ansteigend

: - \frac{1}{4 0 ^{\frac{3}{4}}} < x < 0,

Ansteigend

: 0 < x < \frac{1}{4 0 ^{\frac{3}{4}}},

Absteigend

: \frac{1}{4 0 ^{\frac{3}{4}}} < x < \infty

Stecke

x = - \frac{1}{1 0 ^{\frac{1}{4}} \cdot 4 5}

in

- 8 x^{\frac{5}{3}} + 3 x : - 8 (- \frac{1}{4 \cdot 1 0 ^{\frac{1}{4}} 5})^{\frac{5}{3}} - (\frac{1}{4 \cdot 1 0 ^{\frac{1}{4}} 5})^{\frac{1}{3}}

Minimum (- \frac{1}{1 0 ^{\frac{1}{4}} \cdot 4 5}, - 8 (- \frac{1}{4 \cdot 1 0 ^{\frac{1}{4}} 5})^{\frac{5}{3}} - (\frac{1}{4 \cdot 1 0 ^{\frac{1}{4}} 5})^{\frac{1}{3}})

Stecke

x = \frac{1}{1 0 ^{\frac{1}{4}} \cdot 4 5}

in

- 8 x^{\frac{5}{3}} + 3 x : - 8 (\frac{1}{1 0 ^{\frac{1}{4}} \cdot 4 5})^{\frac{5}{3}} + 3 \frac{1}{1 0 ^{\frac{1}{4}} \cdot 4 5}

Maximum (\frac{1}{1 0 ^{\frac{1}{4}} \cdot 4 5}, - 8 (\frac{1}{1 0 ^{\frac{1}{4}} \cdot 4 5})^{\frac{5}{3}} + 3 \frac{1}{1 0 ^{\frac{1}{4}} \cdot 4 5})

Minimum (- \frac{1}{1 0 ^{\frac{1}{4}} \cdot 4 5}, - 8 (- \frac{1}{4 \cdot 1 0 ^{\frac{1}{4}} 5})^{\frac{5}{3}} - (\frac{1}{4 \cdot 1 0 ^{\frac{1}{4}} 5})^{\frac{1}{3}}), Maximum (\frac{1}{1 0 ^{\frac{1}{4}} \cdot 4 5}, - 8 (\frac{1}{1 0 ^{\frac{1}{4}} \cdot 4 5})^{\frac{5}{3}} + 3 \frac{1}{1 0 ^{\frac{1}{4}} \cdot 4 5})

Graph

Beliebte Beispiele

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