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Beliebt Funktionen >

extreme f(x)=4x^3-108x^2+729x

Lösung

extrempunkte

f (x) = 4 x^{3} - 108 x^{2} + 729 x

Lösung

Maximum (\frac{9}{2}, 1458), Minimum (\frac{27}{2}, 0)

Schritte zur Lösung

f^{'} (x) = 12 x^{2} - 216 x + 729

Intervalle finden:

Ansteigend

: - \infty < x < \frac{9}{2},

Absteigend

: \frac{9}{2} < x < \frac{27}{2},

Ansteigend

: \frac{27}{2} < x < \infty

Stecke

x = \frac{9}{2}

in

4 x^{3} - 108 x^{2} + 729 x : 1458

Maximum (\frac{9}{2}, 1458)

Stecke

x = \frac{27}{2}

in

4 x^{3} - 108 x^{2} + 729 x : 0

Minimum (\frac{27}{2}, 0)

Maximum (\frac{9}{2}, 1458), Minimum (\frac{27}{2}, 0)

Graph

Beliebte Beispiele

extreme f(x)=4x^{3/4}-x,0<= x<= 256

e x t re m e f (x) = 4 x^{\frac{3}{4}} - x, 0 \leq x \leq 256

extreme-x^3+6x^2+15x+4

e x t re m e - x^{3} + 6 x^{2} + 15 x + 4

extreme f(x)=xsqrt(x+8)

e x t re m e f (x) = x x + 8

extreme f(x)=(x+2)/(x^2-3x-10)

e x t re m e f (x) = \frac{x + 2}{x ^{2} - 3 x - 10}

extreme f(x)=(x^2-2x)e^{-x}

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