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Beliebt Funktionen >

extreme f(x)=f(x)=x^3-4x^2-3x+1

Lösung

extrempunkte

f (x) = f (x) = x^{3} - 4 x^{2} - 3 x + 1

Lösung

Maximum (- \frac{1}{3}, \frac{41}{27}), Minimum (3, - 17)

Schritte zur Lösung

f^{'} (x) = 3 x^{2} - 8 x - 3

Intervalle finden:

Ansteigend

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

Absteigend

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

Ansteigend

: 3 < x < \infty

Stecke

x = - \frac{1}{3}

in

x^{3} - 4 x^{2} - 3 x + 1 : \frac{41}{27}

Maximum (- \frac{1}{3}, \frac{41}{27})

Stecke

x = 3

in

x^{3} - 4 x^{2} - 3 x + 1 : - 17

Minimum (3, - 17)

Maximum (- \frac{1}{3}, \frac{41}{27}), Minimum (3, - 17)

Graph

Beliebte Beispiele

extreme f(x)=x^3+3x^2-189x

e x t re m e f (x) = x^{3} + 3 x^{2} - 189 x

extreme f(x)=1-|x-7|

e x t re m e f (x) = 1 - ∣ x - 7 ∣

extreme f(x,y)=(x^2-49)^2+(y^2-9)^2

e x t re m e f (x, y) = (x^{2} - 49)^{2} + (y^{2} - 9)^{2}

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

e x t re m e f (x) = 12 x^{2} - x^{3}

extreme x^3-3x+1,-3/2 <= x<= 3

e x t re m e x^{3} - 3 x + 1, - \frac{3}{2} \leq x \leq 3