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Beliebt Funktionen >

extreme f(x)=-1/6 x^3+3/2 x^2+5/2 x-11/6

Lösung

extrempunkte

f (x) = - \frac{1}{6} x^{3} + \frac{3}{2} x^{2} + \frac{5}{2} x - \frac{11}{6}

Lösung

Minimum (3 - 14, \frac{2 ( 22 - 7 14 )}{3}), Maximum (3 + 14, \frac{2 ( 22 + 7 14 )}{3})

Schritte zur Lösung

f^{'} (x) = \frac{- x ^{2} + 6 x + 5}{2}

Intervalle finden:

Absteigend

: - \infty < x < - 14 + 3,

Ansteigend

: - 14 + 3 < x < 14 + 3,

Absteigend

: 14 + 3 < x < \infty

Stecke

x = 3 - 14

in

- \frac{1}{6} x^{3} + \frac{3}{2} x^{2} + \frac{5}{2} x - \frac{11}{6} : \frac{2 ( 22 - 7 14 )}{3}

Minimum (3 - 14, \frac{2 ( 22 - 7 14 )}{3})

Stecke

x = 3 + 14

in

- \frac{1}{6} x^{3} + \frac{3}{2} x^{2} + \frac{5}{2} x - \frac{11}{6} : \frac{2 ( 22 + 7 14 )}{3}

Maximum (3 + 14, \frac{2 ( 22 + 7 14 )}{3})

Minimum (3 - 14, \frac{2 ( 22 - 7 14 )}{3}), Maximum (3 + 14, \frac{2 ( 22 + 7 14 )}{3})

Graph

Beliebte Beispiele

extreme f(x)=3x-t

e x t re m e f (x) = 3 x - t

extreme f(x)=-4x^{5/3}+7\sqrt[3]{x}

e x t re m e f (x) = - 4 x^{\frac{5}{3}} + 7 3 x

extreme f(x)=(x-5)^2(x+5)

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

extreme f(x,y)=(x^2+y^2)/(x^2y)

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

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

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