extreme f(x)=4x^3-8x

Lösung

extrempunkte

f (x) = 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) = 12 x^{5} + 45 x^{4} - 360 x^{3} + 6

e x t re m e f (x) = (x^{2} + 3 x - 1)^{\frac{1}{3}}

e x t re m e f (x) = x^{3} - 4 x^{2} - x + 1

e x t re m e f (x, y) = \frac{20000}{3 + x ^{2} + y ^{2}}

e x t re m e y = \frac{x}{x ^{2} + 64}