extreme f(x)=(x^2-1)/(x^3)

Lösung

extrempunkte

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

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

Schritte zur Lösung

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

Intervalle finden:

Absteigend

: - \infty < x < - 3,

Ansteigend

: - 3 < x < 0,

Ansteigend

: 0 < x < 3,

Absteigend

: 3 < x < \infty

Stecke

x = - 3

\frac{x ^{2} - 1}{x ^{3}} : - \frac{2}{3 3}

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

Stecke

x = 3

\frac{x ^{2} - 1}{x ^{3}} : \frac{2}{3 3}

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

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

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

e x t re m e f (x) = sin (π x) (- \frac{1}{3}, \frac{1}{3})

e x t re m e f (x) = \frac{x ^{3}}{3} - 3 x^{2} + 8 x - 2, 0 \leq x \leq 3

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

e x t re m e y = 7 + 5 x - 5 x^{2}