extreme f(x)=(1-x^2)/((1+x^2)^2)

Lösung

extrempunkte

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

Minimum (- 3, - \frac{1}{8}), Maximum (0, 1), Minimum (3, - \frac{1}{8})

Schritte zur Lösung

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

Intervalle finden:

Absteigend

: - \infty < x < - 3,

Ansteigend

: - 3 < x < 0,

Absteigend

: 0 < x < 3,

Ansteigend

: 3 < x < \infty

Stecke

x = - 3

\frac{1 - x ^{2}}{( 1 + x ^{2} ) ^{2}} : - \frac{1}{8}

Minimum (- 3, - \frac{1}{8})

Stecke

x = 0

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

Maximum (0, 1)

Stecke

x = 3

\frac{1 - x ^{2}}{( 1 + x ^{2} ) ^{2}} : - \frac{1}{8}

Minimum (3, - \frac{1}{8})

Minimum (- 3, - \frac{1}{8}), Maximum (0, 1), Minimum (3, - \frac{1}{8})

e x t re m e f (x) = 15 x^{\frac{2}{3}} - 10 x

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

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

e x t re m e P (y, x) = - y^{3} - 2 y^{2} - x y

e x t re m e x 2 - x