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

Lösung

extrempunkte

f (x) = (x + 1)^{5} - 5 x - 2

Maximum (- 2, 7), Minimum (0, - 1)

Schritte zur Lösung

f^{'} (x) = 5 x^{4} + 20 x^{3} + 30 x^{2} + 20 x

Intervalle finden:

Ansteigend

: - \infty < x < - 2,

Absteigend

: - 2 < x < 0,

Ansteigend

: 0 < x < \infty

Stecke

x = - 2

(x + 1)^{5} - 5 x - 2 : 7

Maximum (- 2, 7)

Stecke

x = 0

(x + 1)^{5} - 5 x - 2 : - 1

Minimum (0, - 1)

Maximum (- 2, 7), Minimum (0, - 1)

e x t re m e f (x) = \frac{- 5 x ^{2} + 16 x}{2 4 - x}

e x t re m e f (x) = x^{3} - 3 x^{2} - 3 x - 1

e x t re m e f (x) = 4 x^{2} - 8 x + 3

e x t re m e f (x, y) = x^{2} + x y + \frac{1}{2} y^{2} - 5 x + y

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