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Beliebt Funktionen >

extreme f(x)=-4x^3+12x^2

Lösung

extrempunkte

f (x) = - 4 x^{3} + 12 x^{2}

Lösung

Minimum (0, 0), Maximum (2, 16)

Schritte zur Lösung

f^{'} (x) = - 12 x^{2} + 24 x

Intervalle finden:

Absteigend

: - \infty < x < 0,

Ansteigend

: 0 < x < 2,

Absteigend

: 2 < x < \infty

Stecke

x = 0

in

- 4 x^{3} + 12 x^{2} : 0

Minimum (0, 0)

Stecke

x = 2

in

- 4 x^{3} + 12 x^{2} : 16

Maximum (2, 16)

Minimum (0, 0), Maximum (2, 16)

Graph

Beliebte Beispiele

extreme f(x)=(8x)/(x^2+16)

e x t re m e f (x) = \frac{8 x}{x ^{2} + 16}

extreme ((x^2-1))/((x-3)^2)

e x t re m e \frac{( x ^{2} - 1 )}{( x - 3 ) ^{2}}

extreme s(t)=-4.9t^2+29t+2

e x t re m e s (t) = - 4.9 t^{2} + 29 t + 2

extreme y=(x+3)^2-7

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

extreme f(x)=3x-1/2 x^2-1/2 ln(x)

e x t re m e f (x) = 3 x - \frac{1}{2} x^{2} - \frac{1}{2} ln (x)