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Beliebt Funktionen >

extreme x^{25/3}-6x^{19/3}

Lösung

extrempunkte

x^{\frac{25}{3}} - 6 x^{\frac{19}{3}}

Lösung

Maximum - \frac{11 4 ^{\frac{1}{2}}}{5}, (- \frac{11 4 ^{\frac{1}{2}}}{5})^{\frac{25}{3}} - 6 (- \frac{11 4 ^{\frac{1}{2}}}{5})^{\frac{19}{3}}, Sattel (0, 0), Minimum \frac{11 4 ^{\frac{1}{2}}}{5}, (\frac{11 4 ^{\frac{1}{2}}}{5})^{\frac{25}{3}} - 6 (\frac{11 4 ^{\frac{1}{2}}}{5})^{\frac{19}{3}}

Schritte zur Lösung

Bestimme den kritischen Punkt:

x = - \frac{11 4 ^{\frac{1}{2}}}{5}, x = 0, x = \frac{11 4 ^{\frac{1}{2}}}{5}

Bereich von

x^{\frac{25}{3}} - 6 x^{\frac{19}{3}} : - \infty < x < \infty

Intervalle finden:

Ansteigend

: - \infty < x < - \frac{11 4 ^{\frac{1}{2}}}{5},

Absteigend

: - \frac{11 4 ^{\frac{1}{2}}}{5} < x < 0,

Absteigend

: 0 < x < \frac{11 4 ^{\frac{1}{2}}}{5},

Ansteigend

: \frac{11 4 ^{\frac{1}{2}}}{5} < x < \infty

Setz die Extremwerte

x = - \frac{11 4 ^{\frac{1}{2}}}{5}

in

x^{\frac{25}{3}} - 6 x^{\frac{19}{3}} \Rightarrow y = (- \frac{11 4 ^{\frac{1}{2}}}{5})^{\frac{25}{3}} - 6 (- \frac{11 4 ^{\frac{1}{2}}}{5})^{\frac{19}{3}}

ein

Maximum - \frac{11 4 ^{\frac{1}{2}}}{5}, (- \frac{11 4 ^{\frac{1}{2}}}{5})^{\frac{25}{3}} - 6 (- \frac{11 4 ^{\frac{1}{2}}}{5})^{\frac{19}{3}}

Setz die Extremwerte

x = 0

in

x^{\frac{25}{3}} - 6 x^{\frac{19}{3}} \Rightarrow y = 0

ein

Sattel (0, 0)

Setz die Extremwerte

x = \frac{11 4 ^{\frac{1}{2}}}{5}

in

x^{\frac{25}{3}} - 6 x^{\frac{19}{3}} \Rightarrow y = (\frac{11 4 ^{\frac{1}{2}}}{5})^{\frac{25}{3}} - 6 (\frac{11 4 ^{\frac{1}{2}}}{5})^{\frac{19}{3}}

ein

Minimum \frac{11 4 ^{\frac{1}{2}}}{5}, (\frac{11 4 ^{\frac{1}{2}}}{5})^{\frac{25}{3}} - 6 (\frac{11 4 ^{\frac{1}{2}}}{5})^{\frac{19}{3}}

Maximum - \frac{11 4 ^{\frac{1}{2}}}{5}, (- \frac{11 4 ^{\frac{1}{2}}}{5})^{\frac{25}{3}} - 6 (- \frac{11 4 ^{\frac{1}{2}}}{5})^{\frac{19}{3}}, Sattel (0, 0), Minimum \frac{11 4 ^{\frac{1}{2}}}{5}, (\frac{11 4 ^{\frac{1}{2}}}{5})^{\frac{25}{3}} - 6 (\frac{11 4 ^{\frac{1}{2}}}{5})^{\frac{19}{3}}

Graph

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