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Beliebt Funktionen >

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

Lösung

extrempunkte

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

Lösung

Maximum (- 2, 0), Minimum (\frac{4}{3}, - \frac{500}{27})

Schritte zur Lösung

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

Intervalle finden:

Ansteigend

: - \infty < x < - 2,

Absteigend

: - 2 < x < \frac{4}{3},

Ansteigend

: \frac{4}{3} < x < \infty

Stecke

x = - 2

in

(x + 2)^{2} (x - 3) : 0

Maximum (- 2, 0)

Stecke

x = \frac{4}{3}

in

(x + 2)^{2} (x - 3) : - \frac{500}{27}

Minimum (\frac{4}{3}, - \frac{500}{27})

Maximum (- 2, 0), Minimum (\frac{4}{3}, - \frac{500}{27})

Graph

Beliebte Beispiele

extreme y=x^5-5x^4

e x t re m e y = x^{5} - 5 x^{4}

extreme f(x)=x^3+3x^2,-5/2 <= x<= 1

e x t re m e f (x) = x^{3} + 3 x^{2}, - \frac{5}{2} \leq x \leq 1

extreme 1/((x+1)(x+2)(x+3))

e x t re m e \frac{1}{( x + 1 ) ( x + 2 ) ( x + 3 )}

extreme f(x)=3x^2+10x-5

e x t re m e f (x) = 3 x^{2} + 10 x - 5

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

e x t re m e f (x, y) = - x^{2} - 4 x - y^{2} + 2 y - 1