extreme y=(x+5)/(x^2-4)

Lösung

extrempunkte

y = \frac{x + 5}{x ^{2} - 4}

Minimum (- 5 - 21, - \frac{5 - 21}{8}), Maximum (- 5 + 21, - \frac{21 + 5}{8})

Schritte zur Lösung

f^{'} (x) = \frac{- x ^{2} - 10 x - 4}{( x ^{2} - 4 ) ^{2}}

Intervalle finden:

Absteigend

: - \infty < x < - 5 - 21,

Ansteigend

: - 5 - 21 < x < - 2,

Ansteigend

: - 2 < x < - 5 + 21,

Absteigend

: - 5 + 21 < x < 2,

Absteigend

: 2 < x < \infty

Stecke

x = - 5 - 21

\frac{x + 5}{x ^{2} - 4} : - \frac{5 - 21}{8}

Minimum (- 5 - 21, - \frac{5 - 21}{8})

Stecke

x = - 5 + 21

\frac{x + 5}{x ^{2} - 4} : - \frac{21 + 5}{8}

Maximum (- 5 + 21, - \frac{21 + 5}{8})

Minimum (- 5 - 21, - \frac{5 - 21}{8}), Maximum (- 5 + 21, - \frac{21 + 5}{8})

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

e x t re m e f (x) = x^{2} - 16 x, - 4 \leq x \leq 4

e x t re m e f (x) = e^{x} (x + 4)

e x t re m e f (x) = (x - 4) (x + 1) (x + 4)

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