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Beliebt Funktionen >

extreme f(x)= 1/8 (x+4)^2(6-x)

Lösung

extrempunkte

f (x) = \frac{1}{8} (x + 4)^{2} (6 - x)

Lösung

Minimum (- 4, 0), Maximum (\frac{8}{3}, \frac{500}{27})

Schritte zur Lösung

f^{'} (x) = \frac{- 3 x ^{2} - 4 x + 32}{8}

Intervalle finden:

Absteigend

: - \infty < x < - 4,

Ansteigend

: - 4 < x < \frac{8}{3},

Absteigend

: \frac{8}{3} < x < \infty

Stecke

x = - 4

in

\frac{1}{8} (x + 4)^{2} (6 - x) : 0

Minimum (- 4, 0)

Stecke

x = \frac{8}{3}

in

\frac{1}{8} (x + 4)^{2} (6 - x) : \frac{500}{27}

Maximum (\frac{8}{3}, \frac{500}{27})

Minimum (- 4, 0), Maximum (\frac{8}{3}, \frac{500}{27})

Graph

Beliebte Beispiele

extreme f(x)=ln((4x^2)/(ln(x)))

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

extreme f(x)=-x^3+3x^2+9x-27

e x t re m e f (x) = - x^{3} + 3 x^{2} + 9 x - 27

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

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

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

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

extreme f(x)=(x^2+2)/(x^2-9)

e x t re m e f (x) = \frac{x ^{2} + 2}{x ^{2} - 9}