extreme f(x)=-2/3 x^3+2x^2+6x+6

Lösung

extrempunkte

f (x) = - \frac{2}{3} x^{3} + 2 x^{2} + 6 x + 6

Minimum (- 1, \frac{8}{3}), Maximum (3, 24)

Schritte zur Lösung

f^{'} (x) = - 2 x^{2} + 4 x + 6

Intervalle finden:

Absteigend

: - \infty < x < - 1,

Ansteigend

: - 1 < x < 3,

Absteigend

: 3 < x < \infty

Stecke

x = - 1

- \frac{2}{3} x^{3} + 2 x^{2} + 6 x + 6 : \frac{8}{3}

Minimum (- 1, \frac{8}{3})

Stecke

x = 3

- \frac{2}{3} x^{3} + 2 x^{2} + 6 x + 6 : 24

Maximum (3, 24)

Minimum (- 1, \frac{8}{3}), Maximum (3, 24)

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

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

roo t s 32 x y

e x t re m e f (x) = ∣ sin (x) ∣

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