extreme y=4x^3-8x

Lösung

extrempunkte

y = 4 x^{3} - 8 x

Maximum (- \frac{2}{3}, - 4 (\frac{2}{3})^{\frac{3}{2}} + 8 \frac{2}{3}), Minimum (\frac{2}{3}, 4 (\frac{2}{3})^{\frac{3}{2}} - 8 \frac{2}{3})

Schritte zur Lösung

f^{'} (x) = 12 x^{2} - 8

Intervalle finden:

Ansteigend

: - \infty < x < - \frac{2}{3},

Absteigend

: - \frac{2}{3} < x < \frac{2}{3},

Ansteigend

: \frac{2}{3} < x < \infty

Stecke

x = - \frac{2}{3}

4 x^{3} - 8 x : - 4 (\frac{2}{3})^{\frac{3}{2}} + 8 \frac{2}{3}

Maximum (- \frac{2}{3}, - 4 (\frac{2}{3})^{\frac{3}{2}} + 8 \frac{2}{3})

Stecke

x = \frac{2}{3}

4 x^{3} - 8 x : 4 (\frac{2}{3})^{\frac{3}{2}} - 8 \frac{2}{3}

Minimum (\frac{2}{3}, 4 (\frac{2}{3})^{\frac{3}{2}} - 8 \frac{2}{3})

Maximum (- \frac{2}{3}, - 4 (\frac{2}{3})^{\frac{3}{2}} + 8 \frac{2}{3}), Minimum (\frac{2}{3}, 4 (\frac{2}{3})^{\frac{3}{2}} - 8 \frac{2}{3})

e x t re m e f (x) = \frac{7}{4 - 3 sin ^{2} ( x )}

e x t re m e x^{2} - 5, 1 < x < 7

e x t re m e (x - 7) (x - 5)^{2} (x - 3) (x - 1)

e x t re m e \frac{400}{1 + 8 e ^{0.05 x}}

e x t re m e 1 + (ln (x))