extreme y=x^{6/7}(x^2-4)

Lösung

extrempunkte

y = x^{\frac{6}{7}} (x^{2} - 4)

Minimum - (\frac{6}{5})^{\frac{1}{2}}, - \frac{14 ( - ( \frac{6}{5} ) ^{\frac{1}{2}} ) ^{\frac{6}{7}}}{5}, Maximum (0, 0), Minimum ((\frac{6}{5})^{\frac{1}{2}}, - \frac{14 \cdot 6 ^{\frac{3}{7}}}{5 \cdot 5 ^{\frac{3}{7}}})

Schritte zur Lösung

f^{'} (x) = \frac{4 ( 5 ^{\frac{1}{2}} x + 6 ^{\frac{1}{2}} ) ( 5 ^{\frac{1}{2}} x - 6 ^{\frac{1}{2}} )}{7 x ^{\frac{1}{7}}}

Intervalle finden:

Absteigend

: - \infty < x < - (\frac{6}{5})^{\frac{1}{2}},

Ansteigend

: - (\frac{6}{5})^{\frac{1}{2}} < x < 0,

Absteigend

: 0 < x < (\frac{6}{5})^{\frac{1}{2}},

Ansteigend

: (\frac{6}{5})^{\frac{1}{2}} < x < \infty

Stecke

x = - (\frac{6}{5})^{\frac{1}{2}}

x^{\frac{6}{7}} (x^{2} - 4) : - \frac{14 ( - ( \frac{6}{5} ) ^{\frac{1}{2}} ) ^{\frac{6}{7}}}{5}

Minimum - (\frac{6}{5})^{\frac{1}{2}}, - \frac{14 ( - ( \frac{6}{5} ) ^{\frac{1}{2}} ) ^{\frac{6}{7}}}{5}

Stecke

x = 0

x^{\frac{6}{7}} (x^{2} - 4) : 0

Maximum (0, 0)

Stecke

x = (\frac{6}{5})^{\frac{1}{2}}

x^{\frac{6}{7}} (x^{2} - 4) : - \frac{14 \cdot 6 ^{\frac{3}{7}}}{5 \cdot 5 ^{\frac{3}{7}}}

Minimum ((\frac{6}{5})^{\frac{1}{2}}, - \frac{14 \cdot 6 ^{\frac{3}{7}}}{5 \cdot 5 ^{\frac{3}{7}}})

Minimum - (\frac{6}{5})^{\frac{1}{2}}, - \frac{14 ( - ( \frac{6}{5} ) ^{\frac{1}{2}} ) ^{\frac{6}{7}}}{5}, Maximum (0, 0), Minimum ((\frac{6}{5})^{\frac{1}{2}}, - \frac{14 \cdot 6 ^{\frac{3}{7}}}{5 \cdot 5 ^{\frac{3}{7}}})

e x t re m e f (x) = 3 x^{3} - 3 x^{2} - 3 x + 2

e x t re m e f (x, y) = x^{2} + (y - 1)^{2}

e x t re m e f (x) = \frac{( x ^{2} - 7 )}{x - 4}

e x t re m e \frac{x ^{2} + 1}{x ^{2} - 1}

e x t re m e f (x) = \frac{x ^{2} - 12}{x - 4}