extreme f(x)=x^5-5x^4+5x^3-10

Lösung

extrempunkte

f (x) = x^{5} - 5 x^{4} + 5 x^{3} - 10

Sattel (0, - 10), Maximum (1, - 9), Minimum (3, - 37)

Schritte zur Lösung

f^{'} (x) = 5 x^{4} - 20 x^{3} + 15 x^{2}

Intervalle finden:

Ansteigend

: - \infty < x < 0,

Ansteigend

: 0 < x < 1,

Absteigend

: 1 < x < 3,

Ansteigend

: 3 < x < \infty

Stecke

x = 0

x^{5} - 5 x^{4} + 5 x^{3} - 10 : - 10

Sattel (0, - 10)

Stecke

x = 1

x^{5} - 5 x^{4} + 5 x^{3} - 10 : - 9

Maximum (1, - 9)

Stecke

x = 3

x^{5} - 5 x^{4} + 5 x^{3} - 10 : - 37

Minimum (3, - 37)

Sattel (0, - 10), Maximum (1, - 9), Minimum (3, - 37)

e x t re m e f (x) = 8 x - 8 ln (x^{2}), (0, + \infty)

e x t re m e f (x, y) = 7 x^{2} y - 8 x y^{3} + 9 y^{3}

e x t re m e \frac{8 - x ^{3}}{x ^{2}}

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

e x t re m e f (x) = \frac{2 - x ^{2}}{2 x + 1} + 7