extreme 5+6x-8x^3

Lösung

extrempunkte

5 + 6 x - 8 x^{3}

Minimum (- \frac{1}{2}, 3), Maximum (\frac{1}{2}, 7)

Schritte zur Lösung

f^{'} (x) = - 24 x^{2} + 6

Intervalle finden:

Absteigend

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

Ansteigend

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

Absteigend

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

Stecke

x = - \frac{1}{2}

5 + 6 x - 8 x^{3} : 3

Minimum (- \frac{1}{2}, 3)

Stecke

x = \frac{1}{2}

5 + 6 x - 8 x^{3} : 7

Maximum (\frac{1}{2}, 7)

Minimum (- \frac{1}{2}, 3), Maximum (\frac{1}{2}, 7)

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

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

e x t re m e f (1) = x^{3} - 6 x^{2} + 9 x + 2

e x t re m e f (x) = \frac{2}{3} x^{3} + \frac{11}{2} x^{2} - 21 x + 5

e x t re m e f (x) = (x - 3) e^{- 5 x}