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Beliebt Funktionen >

extreme f(x)=x^3-4x^2+4x+1

Lösung

extrempunkte

f (x) = x^{3} - 4 x^{2} + 4 x + 1

Lösung

Maximum (\frac{2}{3}, \frac{59}{27}), Minimum (2, 1)

Schritte zur Lösung

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

Intervalle finden:

Ansteigend

: - \infty < x < \frac{2}{3},

Absteigend

: \frac{2}{3} < x < 2,

Ansteigend

: 2 < x < \infty

Stecke

x = \frac{2}{3}

in

x^{3} - 4 x^{2} + 4 x + 1 : \frac{59}{27}

Maximum (\frac{2}{3}, \frac{59}{27})

Stecke

x = 2

in

x^{3} - 4 x^{2} + 4 x + 1 : 1

Minimum (2, 1)

Maximum (\frac{2}{3}, \frac{59}{27}), Minimum (2, 1)

Graph

Beliebte Beispiele

interzeption f(x)=-2

in t erce pt s f (x) = - 2

bereich f(x)=2sqrt(x+1)-3

r an g e f (x) = 2 x + 1 - 3

asymptoten f(x)=((x^2+x+2))/(x-1)

a sy m pt o t es f (x) = \frac{( x ^{2} + x + 2 )}{x - 1}

symmetrie (x-1)^2+2

sy mm e t ry (x - 1)^{2} + 2

domäne f(x)=x+sqrt(x)+1

d o main f (x) = x + x + 1