extreme f(x)=x^5-10x^4+2=x^4(x-10)+2

Lösung

extrempunkte

f (x) = x^{5} - 10 x^{4} + 2 = x^{4} (x - 10) + 2

Maximum (0, 2), Minimum (8, - 8190)

Schritte zur Lösung

f^{'} (x) = 5 x^{3} (x - 8)

Intervalle finden:

Ansteigend

: - \infty < x < 0,

Absteigend

: 0 < x < 8,

Ansteigend

: 8 < x < \infty

Stecke

x = 0

x^{4} (x - 10) + 2 : 2

Maximum (0, 2)

Stecke

x = 8

x^{4} (x - 10) + 2 : - 8190

Minimum (8, - 8190)

Maximum (0, 2), Minimum (8, - 8190)

e x t re m e f (x) = x^{9} - x^{7}

e x t re m e 3 x^{4} + 3 y^{4} - 2 x y

e x t re m e f (x) = 150 x + 18 x^{2} - 1.5 x^{3}

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

e x t re m e f (x) = 2 x - 4 cos (x), - 2 \leq x \leq 0