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Beliebt Funktionen >

extreme f(x)=(2-x^2)^{3/2}

Lösung

extrempunkte

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

Lösung

Minimum (- 2, 0), Maximum (0, 2 \cdot 2^{\frac{1}{2}}), Minimum (2, 0)

Schritte zur Lösung

f^{'} (x) = - 3 x (2 - x^{2})^{\frac{1}{2}}

Intervalle finden:

Ansteigend

: - 2^{\frac{1}{2}} < x < 0,

Absteigend

: 0 < x < 2^{\frac{1}{2}}

Stecke

x = - 2

in

(2 - x^{2})^{\frac{3}{2}} : 0

Minimum (- 2, 0)

Stecke

x = 0

in

(2 - x^{2})^{\frac{3}{2}} : 2 \cdot 2^{\frac{1}{2}}

Maximum (0, 2 \cdot 2^{\frac{1}{2}})

Stecke

x = 2

in

(2 - x^{2})^{\frac{3}{2}} : 0

Minimum (2, 0)

Minimum (- 2, 0), Maximum (0, 2 \cdot 2^{\frac{1}{2}}), Minimum (2, 0)

Graph

Beliebte Beispiele

extreme f(x)=6x^2-8x+2

e x t re m e f (x) = 6 x^{2} - 8 x + 2

extreme f(x)=|2x+1|

e x t re m e f (x) = ∣ 2 x + 1 ∣

extreme f(x,y)=e^{2x}(x+y^2+2y)+10

e x t re m e f (x, y) = e^{2 x} (x + y^{2} + 2 y) + 10

extreme P(x,y)=x^2-y^2

e x t re m e P (x, y) = x^{2} - y^{2}

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

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