extreme f(x)=x^3-5x^2-8x-8

Lösung

extrempunkte

f (x) = x^{3} - 5 x^{2} - 8 x - 8

Maximum (- \frac{2}{3}, - \frac{140}{27}), Minimum (4, - 56)

Schritte zur Lösung

f^{'} (x) = 3 x^{2} - 10 x - 8

Intervalle finden:

Ansteigend

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

Absteigend

: - \frac{2}{3} < x < 4,

Ansteigend

: 4 < x < \infty

Stecke

x = - \frac{2}{3}

x^{3} - 5 x^{2} - 8 x - 8 : - \frac{140}{27}

Maximum (- \frac{2}{3}, - \frac{140}{27})

Stecke

x = 4

x^{3} - 5 x^{2} - 8 x - 8 : - 56

Minimum (4, - 56)

Maximum (- \frac{2}{3}, - \frac{140}{27}), Minimum (4, - 56)

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

e x t re m e y = x^{\frac{2}{5}} (x + 3)

e x t re m e x + 2 cos (x)

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

e x t re m e f (x, y) = - x^{2} + 5 y^{2} - 7 x + 2 y + 5