extreme f(x)=(-4x)/(x^2+3)

Lösung

extrempunkte

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

Maximum (- 3, \frac{2}{3}), Minimum (3, - \frac{2}{3})

Schritte zur Lösung

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

Intervalle finden:

Ansteigend

: - \infty < x < - 3,

Absteigend

: - 3 < x < 3,

Ansteigend

: 3 < x < \infty

Stecke

x = - 3

\frac{- 4 x}{x ^{2} + 3} : \frac{2}{3}

Maximum (- 3, \frac{2}{3})

Stecke

x = 3

\frac{- 4 x}{x ^{2} + 3} : - \frac{2}{3}

Minimum (3, - \frac{2}{3})

Maximum (- 3, \frac{2}{3}), Minimum (3, - \frac{2}{3})

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

e x t re m e f (x) = cos (π x), 0 \leq x \leq \frac{2}{3}

e x t re m e f (x) = x^{3} + x^{2} + 8 x + 6

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

e x t re m e x^{2} + x y + y^{2} - 28 y + 261