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Beliebt Funktionen >

extreme (1-x^2)^2

Lösung

extrempunkte

(1 - x^{2})^{2}

Lösung

Minimum (- 1, 0), Maximum (0, 1), Minimum (1, 0)

Schritte zur Lösung

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

Intervalle finden:

Absteigend

: - \infty < x < - 1,

Ansteigend

: - 1 < x < 0,

Absteigend

: 0 < x < 1,

Ansteigend

: 1 < x < \infty

Stecke

x = - 1

in

(1 - x^{2})^{2} : 0

Minimum (- 1, 0)

Stecke

x = 0

in

(1 - x^{2})^{2} : 1

Maximum (0, 1)

Stecke

x = 1

in

(1 - x^{2})^{2} : 0

Minimum (1, 0)

Minimum (- 1, 0), Maximum (0, 1), Minimum (1, 0)

Graph

Beliebte Beispiele

extreme f(x)=-10/3 x^3-19x^2-24x+50

e x t re m e f (x) = - \frac{10}{3} x^{3} - 19 x^{2} - 24 x + 50

extreme y=4cos(x/2)+2

e x t re m e y = 4 cos (\frac{x}{2}) + 2

extreme K(r,s)=5r-s

e x t re m e K (r, s) = 5 r - s

extreme f(x)=20x^3-3x^5

e x t re m e f (x) = 20 x^{3} - 3 x^{5}

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

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