extreme f(x)=(x^2+1)/(x^2-25)

Lösung

extrempunkte

f (x) = \frac{x ^{2} + 1}{x ^{2} - 25}

Maximum (0, - \frac{1}{25})

Schritte zur Lösung

f^{'} (x) = - \frac{52 x}{( x ^{2} - 25 ) ^{2}}

Intervalle finden:

Ansteigend

: - \infty < x < - 5,

Ansteigend

: - 5 < x < 0,

Absteigend

: 0 < x < 5,

Absteigend

: 5 < x < \infty

Stecke

x = 0

\frac{x ^{2} + 1}{x ^{2} - 25} : - \frac{1}{25}

Maximum (0, - \frac{1}{25})

e x t re m e 2 x^{3} - x^{2} - 4 x + 4

e x t re m e f (x, y) = \frac{2}{x} + \frac{1}{y} + x y

e x t re m e f (x) = 26 x^{2} + 80 x + 64

e x t re m e f (x, y) = x^{3} - y^{2} - 12 x + 4 y + 2

e x t re m e f (x) = - 3 sin^{2} (x), 0 \leq x \leq π