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Beliebt Funktionen >

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

Lösung

extrempunkte

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

Lösung

Maximum (- 6, 100), Minimum (0, 64), Maximum (6, 100)

Schritte zur Lösung

f^{'} (x) = - 4 x (x + 6) (x - 6)

Intervalle finden:

Ansteigend

: - \infty < x < - 6,

Absteigend

: - 6 < x < 0,

Ansteigend

: 0 < x < 6,

Absteigend

: 6 < x < \infty

Stecke

x = - 6

in

(x^{2} + 4) (16 - x^{2}) : 100

Maximum (- 6, 100)

Stecke

x = 0

in

(x^{2} + 4) (16 - x^{2}) : 64

Minimum (0, 64)

Stecke

x = 6

in

(x^{2} + 4) (16 - x^{2}) : 100

Maximum (6, 100)

Maximum (- 6, 100), Minimum (0, 64), Maximum (6, 100)

Graph

Beliebte Beispiele

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

e x t re m e f (x) = x^{4} + x^{3} - 3 x^{2} + 1

e x t re m e f (x) = 9

extreme f(x,y)=(e^{xy})

e x t re m e f (x, y) = (e^{x y})

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

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

extreme f(x)=2x^2+3y^2-4x-5

e x t re m e f (x) = 2 x^{2} + 3 y^{2} - 4 x - 5