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Beliebt Funktionen >

extreme f(x)=-12x^3+2x^2-3

Lösung

extrempunkte

f (x) = - 12 x^{3} + 2 x^{2} - 3

Lösung

Minimum (0, - 3), Maximum (\frac{1}{9}, - \frac{727}{243})

Schritte zur Lösung

f^{'} (x) = - 36 x^{2} + 4 x

Intervalle finden:

Absteigend

: - \infty < x < 0,

Ansteigend

: 0 < x < \frac{1}{9},

Absteigend

: \frac{1}{9} < x < \infty

Stecke

x = 0

in

- 12 x^{3} + 2 x^{2} - 3 : - 3

Minimum (0, - 3)

Stecke

x = \frac{1}{9}

in

- 12 x^{3} + 2 x^{2} - 3 : - \frac{727}{243}

Maximum (\frac{1}{9}, - \frac{727}{243})

Minimum (0, - 3), Maximum (\frac{1}{9}, - \frac{727}{243})

Graph

Beliebte Beispiele

extreme y= 1/2 x^2+((14-3x)/4)^2

e x t re m e y = \frac{1}{2} x^{2} + (\frac{14 - 3 x}{4})^{2}

extreme f(x,y)=x-5y

e x t re m e f (x, y) = x - 5 y

extreme f(x)=x^2-(54)/x

e x t re m e f (x) = x^{2} - \frac{54}{x}

extreme 2x^3+3x^2-36x+3,-3<= x<= 6

e x t re m e 2 x^{3} + 3 x^{2} - 36 x + 3, - 3 \leq x \leq 6

extreme g(t)=-5t^2-3t+2

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