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Beliebt Funktionen >

extreme f(x)=3x-2x^2-(4x^3)/3

Lösung

extrempunkte

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

Lösung

Minimum (- \frac{3}{2}, - \frac{9}{2}), Maximum (\frac{1}{2}, \frac{5}{6})

Schritte zur Lösung

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

Intervalle finden:

Absteigend

: - \infty < x < - \frac{3}{2},

Ansteigend

: - \frac{3}{2} < x < \frac{1}{2},

Absteigend

: \frac{1}{2} < x < \infty

Stecke

x = - \frac{3}{2}

in

3 x - 2 x^{2} - \frac{4 x ^{3}}{3} : - \frac{9}{2}

Minimum (- \frac{3}{2}, - \frac{9}{2})

Stecke

x = \frac{1}{2}

in

3 x - 2 x^{2} - \frac{4 x ^{3}}{3} : \frac{5}{6}

Maximum (\frac{1}{2}, \frac{5}{6})

Minimum (- \frac{3}{2}, - \frac{9}{2}), Maximum (\frac{1}{2}, \frac{5}{6})

Graph

Beliebte Beispiele

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

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

extreme f(x,y)=x^3-6xy+3y^2+1

e x t re m e f (x, y) = x^{3} - 6 x y + 3 y^{2} + 1

extreme f(x)=cos(5x)

e x t re m e f (x) = cos (5 x)

extreme f(x)=cos(4x)

e x t re m e f (x) = cos (4 x)

extreme e^{-1.5x^2}

e x t re m e e^{- 1.5 x^{2}}