extreme f(x)= 1/3 x^3+3x^2+5x-11/3

Lösung

extrempunkte

f (x) = \frac{1}{3} x^{3} + 3 x^{2} + 5 x - \frac{11}{3}

Maximum (- 5, \frac{14}{3}), Minimum (- 1, - 6)

Schritte zur Lösung

f^{'} (x) = x^{2} + 6 x + 5

Intervalle finden:

Ansteigend

: - \infty < x < - 5,

Absteigend

: - 5 < x < - 1,

Ansteigend

: - 1 < x < \infty

Stecke

x = - 5

\frac{1}{3} x^{3} + 3 x^{2} + 5 x - \frac{11}{3} : \frac{14}{3}

Maximum (- 5, \frac{14}{3})

Stecke

x = - 1

\frac{1}{3} x^{3} + 3 x^{2} + 5 x - \frac{11}{3} : - 6

Minimum (- 1, - 6)

Maximum (- 5, \frac{14}{3}), Minimum (- 1, - 6)

e x t re m e f (x) = ∣ x ∣ + x^{2} - 5 x + 6

e x t re m e f (x, y) = 60 x^{\frac{1}{3}} y^{\frac{2}{3}}

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

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

e x t re m e y = x^{5} - 5 x^{4}