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Beliebt Funktionen >

extreme f(x)=-4x^{5/3}+7\sqrt[3]{x}

Lösung

extrempunkte

f (x) = - 4 x^{\frac{5}{3}} + 7 3 x

Lösung

Minimum - \frac{7 ^{\frac{3}{4}}}{2 \cdot 2 ^{\frac{1}{2}} \cdot 5 ^{\frac{3}{4}}}, - 4 (- \frac{7 ^{\frac{3}{4}}}{2 \cdot 2 ^{\frac{1}{2}} \cdot 5 ^{\frac{3}{4}}})^{\frac{5}{3}} - 7 (\frac{7 ^{\frac{3}{4}}}{2 \cdot 2 ^{\frac{1}{2}} \cdot 5 ^{\frac{3}{4}}})^{\frac{1}{3}}, Maximum \frac{7 ^{\frac{3}{4}}}{2 \cdot 2 ^{\frac{1}{2}} \cdot 5 ^{\frac{3}{4}}}, - 4 (\frac{7 ^{\frac{3}{4}}}{2 \cdot 2 ^{\frac{1}{2}} \cdot 5 ^{\frac{3}{4}}})^{\frac{5}{3}} + 7 3 \frac{7 ^{\frac{3}{4}}}{2 \cdot 2 ^{\frac{1}{2}} \cdot 5 ^{\frac{3}{4}}}

Schritte zur Lösung

f^{'} (x) = - \frac{20 x ^{\frac{2}{3}}}{3} + \frac{7}{3 x ^{\frac{2}{3}}}

Intervalle finden:

Absteigend

: - \infty < x < - (\frac{7}{20})^{\frac{3}{4}},

Ansteigend

: - (\frac{7}{20})^{\frac{3}{4}} < x < 0,

Ansteigend

: 0 < x < (\frac{7}{20})^{\frac{3}{4}},

Absteigend

: (\frac{7}{20})^{\frac{3}{4}} < x < \infty

Stecke

x = - \frac{7 ^{\frac{3}{4}}}{2 \cdot 2 ^{\frac{1}{2}} \cdot 5 ^{\frac{3}{4}}}

in

- 4 x^{\frac{5}{3}} + 7 3 x : - 4 (- \frac{7 ^{\frac{3}{4}}}{2 \cdot 2 ^{\frac{1}{2}} \cdot 5 ^{\frac{3}{4}}})^{\frac{5}{3}} - 7 (\frac{7 ^{\frac{3}{4}}}{2 \cdot 2 ^{\frac{1}{2}} \cdot 5 ^{\frac{3}{4}}})^{\frac{1}{3}}

Minimum - \frac{7 ^{\frac{3}{4}}}{2 \cdot 2 ^{\frac{1}{2}} \cdot 5 ^{\frac{3}{4}}}, - 4 (- \frac{7 ^{\frac{3}{4}}}{2 \cdot 2 ^{\frac{1}{2}} \cdot 5 ^{\frac{3}{4}}})^{\frac{5}{3}} - 7 (\frac{7 ^{\frac{3}{4}}}{2 \cdot 2 ^{\frac{1}{2}} \cdot 5 ^{\frac{3}{4}}})^{\frac{1}{3}}

Stecke

x = \frac{7 ^{\frac{3}{4}}}{2 \cdot 2 ^{\frac{1}{2}} \cdot 5 ^{\frac{3}{4}}}

in

- 4 x^{\frac{5}{3}} + 7 3 x : - 4 (\frac{7 ^{\frac{3}{4}}}{2 \cdot 2 ^{\frac{1}{2}} \cdot 5 ^{\frac{3}{4}}})^{\frac{5}{3}} + 7 3 \frac{7 ^{\frac{3}{4}}}{2 \cdot 2 ^{\frac{1}{2}} \cdot 5 ^{\frac{3}{4}}}

Maximum \frac{7 ^{\frac{3}{4}}}{2 \cdot 2 ^{\frac{1}{2}} \cdot 5 ^{\frac{3}{4}}}, - 4 (\frac{7 ^{\frac{3}{4}}}{2 \cdot 2 ^{\frac{1}{2}} \cdot 5 ^{\frac{3}{4}}})^{\frac{5}{3}} + 7 3 \frac{7 ^{\frac{3}{4}}}{2 \cdot 2 ^{\frac{1}{2}} \cdot 5 ^{\frac{3}{4}}}

Minimum - \frac{7 ^{\frac{3}{4}}}{2 \cdot 2 ^{\frac{1}{2}} \cdot 5 ^{\frac{3}{4}}}, - 4 (- \frac{7 ^{\frac{3}{4}}}{2 \cdot 2 ^{\frac{1}{2}} \cdot 5 ^{\frac{3}{4}}})^{\frac{5}{3}} - 7 (\frac{7 ^{\frac{3}{4}}}{2 \cdot 2 ^{\frac{1}{2}} \cdot 5 ^{\frac{3}{4}}})^{\frac{1}{3}}, Maximum \frac{7 ^{\frac{3}{4}}}{2 \cdot 2 ^{\frac{1}{2}} \cdot 5 ^{\frac{3}{4}}}, - 4 (\frac{7 ^{\frac{3}{4}}}{2 \cdot 2 ^{\frac{1}{2}} \cdot 5 ^{\frac{3}{4}}})^{\frac{5}{3}} + 7 3 \frac{7 ^{\frac{3}{4}}}{2 \cdot 2 ^{\frac{1}{2}} \cdot 5 ^{\frac{3}{4}}}

Graph

Beliebte Beispiele

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