extreme f(x)=x^3+2x^2-15x-20

Lösung

extrempunkte

f (x) = x^{3} + 2 x^{2} - 15 x - 20

Maximum (- 3, 16), Minimum (\frac{5}{3}, - \frac{940}{27})

Schritte zur Lösung

f^{'} (x) = 3 x^{2} + 4 x - 15

Intervalle finden:

Ansteigend

: - \infty < x < - 3,

Absteigend

: - 3 < x < \frac{5}{3},

Ansteigend

: \frac{5}{3} < x < \infty

Stecke

x = - 3

x^{3} + 2 x^{2} - 15 x - 20 : 16

Maximum (- 3, 16)

Stecke

x = \frac{5}{3}

x^{3} + 2 x^{2} - 15 x - 20 : - \frac{940}{27}

Minimum (\frac{5}{3}, - \frac{940}{27})

Maximum (- 3, 16), Minimum (\frac{5}{3}, - \frac{940}{27})

e x t re m e f (x, y) = x^{3} + 3 x y^{2} - 15 x - 12 y

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

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

e x t re m e f (x) = 3 x + y

e x t re m e \frac{x ^{2} - 4}{x ^{2} + 4}