extreme y=5+6x-8x^3

Lösung

extrempunkte

y = 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 f (x) = \frac{2 x + 4}{x ^{2} + 4}

e x t re m e f (x) = (6 x + 1) e^{8 x - x^{2}}

e x t re m e f (x) = x^{4} - 3 x^{2}, - 2 \leq x \leq 0

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

e x t re m e y = 15 x e^{- 0.05 x} - 30