extreme f(x)= x/((x^2+4))

Lösung

extrempunkte

f (x) = \frac{x}{( x ^{2} + 4 )}

Minimum (- 2, - \frac{1}{4}), Maximum (2, \frac{1}{4})

Schritte zur Lösung

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

Intervalle finden:

Absteigend

: - \infty < x < - 2,

Ansteigend

: - 2 < x < 2,

Absteigend

: 2 < x < \infty

Stecke

x = - 2

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

Minimum (- 2, - \frac{1}{4})

Stecke

x = 2

\frac{x}{x ^{2} + 4} : \frac{1}{4}

Maximum (2, \frac{1}{4})

Minimum (- 2, - \frac{1}{4}), Maximum (2, \frac{1}{4})

e x t re m e f (x) = - 0.5 x^{2}

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

e x t re m e y = x^{3} - 3 x^{2} - 9 x

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

e x t re m e f (z) = z + z^{3} - 2 z^{2} - 4