extreme x^{1/5}(x^2-4)

Lösung

extrempunkte

x^{\frac{1}{5}} (x^{2} - 4)

Maximum (- \frac{2}{1 1 ^{\frac{1}{2}}}, \frac{40 \cdot 2 ^{\frac{1}{5}}}{11 \cdot 1 1 ^{\frac{1}{10}}}), Minimum (\frac{2}{1 1 ^{\frac{1}{2}}}, - \frac{40 \cdot 2 ^{\frac{1}{5}}}{11 \cdot 1 1 ^{\frac{1}{10}}})

Schritte zur Lösung

f^{'} (x) = \frac{( 1 1 ^{\frac{1}{2}} x + 2 ) ( 1 1 ^{\frac{1}{2}} x - 2 )}{5 x ^{\frac{4}{5}}}

Intervalle finden:

Ansteigend

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

Absteigend

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

Absteigend

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

Ansteigend

: \frac{2}{1 1 ^{\frac{1}{2}}} < x < \infty

Stecke

x = - \frac{2}{1 1 ^{\frac{1}{2}}}

x^{\frac{1}{5}} (x^{2} - 4) : \frac{40 \cdot 2 ^{\frac{1}{5}}}{11 \cdot 1 1 ^{\frac{1}{10}}}

Maximum (- \frac{2}{1 1 ^{\frac{1}{2}}}, \frac{40 \cdot 2 ^{\frac{1}{5}}}{11 \cdot 1 1 ^{\frac{1}{10}}})

Stecke

x = \frac{2}{1 1 ^{\frac{1}{2}}}

x^{\frac{1}{5}} (x^{2} - 4) : - \frac{40 \cdot 2 ^{\frac{1}{5}}}{11 \cdot 1 1 ^{\frac{1}{10}}}

Minimum (\frac{2}{1 1 ^{\frac{1}{2}}}, - \frac{40 \cdot 2 ^{\frac{1}{5}}}{11 \cdot 1 1 ^{\frac{1}{10}}})

Maximum (- \frac{2}{1 1 ^{\frac{1}{2}}}, \frac{40 \cdot 2 ^{\frac{1}{5}}}{11 \cdot 1 1 ^{\frac{1}{10}}}), Minimum (\frac{2}{1 1 ^{\frac{1}{2}}}, - \frac{40 \cdot 2 ^{\frac{1}{5}}}{11 \cdot 1 1 ^{\frac{1}{10}}})

e x t re m e f (x) = cos (\frac{4 x}{3})

e x t re m e \frac{5 x}{1 - x}

e x t re m e K (r, s) = 3 r - 7 s

e x t re m e f (x, y) = - y^{2} + y^{2} x - x^{2} + x

e x t re m e y = x^{3} - 9 x^{2} + 7 x - 6