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Beliebt Funktionen >

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

Lösung

extrempunkte

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

Lösung

Minimum (\frac{3 - 57}{8}, \frac{3 ( 471 - 133 57 )}{512}), Maximum (\frac{3 + 57}{8}, \frac{3 ( 471 + 133 57 )}{512}), Minimum (3, 0)

Schritte zur Lösung

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

Intervalle finden:

Absteigend

: - \infty < x < \frac{3 - 57}{8},

Ansteigend

: \frac{3 - 57}{8} < x < \frac{3 + 57}{8},

Absteigend

: \frac{3 + 57}{8} < x < 3,

Ansteigend

: 3 < x < \infty

Stecke

x = \frac{3 - 57}{8}

in

x (x - 3)^{2} (x + 1) : \frac{3 ( 471 - 133 57 )}{512}

Minimum (\frac{3 - 57}{8}, \frac{3 ( 471 - 133 57 )}{512})

Stecke

x = \frac{3 + 57}{8}

in

x (x - 3)^{2} (x + 1) : \frac{3 ( 471 + 133 57 )}{512}

Maximum (\frac{3 + 57}{8}, \frac{3 ( 471 + 133 57 )}{512})

Stecke

x = 3

in

x (x - 3)^{2} (x + 1) : 0

Minimum (3, 0)

Minimum (\frac{3 - 57}{8}, \frac{3 ( 471 - 133 57 )}{512}), Maximum (\frac{3 + 57}{8}, \frac{3 ( 471 + 133 57 )}{512}), Minimum (3, 0)

Graph

Beliebte Beispiele

extreme f(x)=-4x^2-32x-62

e x t re m e f (x) = - 4 x^{2} - 32 x - 62

extreme f(x,y)=2x^3+6xy^2-3y^3-150x

e x t re m e f (x, y) = 2 x^{3} + 6 x y^{2} - 3 y^{3} - 150 x

extreme (x-2)^2+1

e x t re m e (x - 2)^{2} + 1

extreme f(x)=sin(x),0<= x< pi/2

e x t re m e f (x) = sin (x), 0 \leq x < \frac{π}{2}

extreme f(x)=(x^2-4)^2-4

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