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Beliebt Funktionen >

extreme f(x)=x^4-8x^3+16x^2+6

Lösung

extrempunkte

f (x) = x^{4} - 8 x^{3} + 16 x^{2} + 6

Lösung

Minimum (0, 6), Maximum (2, 22), Minimum (4, 6)

Schritte zur Lösung

f^{'} (x) = 4 x^{3} - 24 x^{2} + 32 x

Intervalle finden:

Absteigend

: - \infty < x < 0,

Ansteigend

: 0 < x < 2,

Absteigend

: 2 < x < 4,

Ansteigend

: 4 < x < \infty

Stecke

x = 0

in

x^{4} - 8 x^{3} + 16 x^{2} + 6 : 6

Minimum (0, 6)

Stecke

x = 2

in

x^{4} - 8 x^{3} + 16 x^{2} + 6 : 22

Maximum (2, 22)

Stecke

x = 4

in

x^{4} - 8 x^{3} + 16 x^{2} + 6 : 6

Minimum (4, 6)

Minimum (0, 6), Maximum (2, 22), Minimum (4, 6)

Graph

Beliebte Beispiele

extreme f(x)=2x^2-10x+5,0<= x<= 7

e x t re m e f (x) = 2 x^{2} - 10 x + 5, 0 \leq x \leq 7

extreme sin(4x)

e x t re m e sin (4 x)

extreme f(x)=((x^2-4x+4))/(x-8)

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

extreme f(x)=(x^3)/3-10x^2+75x+20

e x t re m e f (x) = \frac{x ^{3}}{3} - 10 x^{2} + 75 x + 20

extreme (x^3+1)/(x+1)

e x t re m e \frac{x ^{3} + 1}{x + 1}