extreme (x^2+2)/(x^2-4x)

Lösung

extrempunkte

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

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

Schritte zur Lösung

f^{'} (x) = \frac{- 4 x ^{2} - 4 x + 8}{( x ^{2} - 4 x ) ^{2}}

Intervalle finden:

Absteigend

: - \infty < x < - 2,

Ansteigend

: - 2 < x < 0,

Ansteigend

: 0 < x < 1,

Absteigend

: 1 < x < 4,

Absteigend

: 4 < x < \infty

Stecke

x = - 2

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

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

Stecke

x = 1

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

Maximum (1, - 1)

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

e x t re m e f (x, y) = x^{2} + y^{2} - 5 x + 4 y + x y

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

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

e x t re m e f (x) = x + \frac{25}{x}, 0.2 \leq x \leq 20

e x t re m e y = x^{3} - 30 x^{2} + 6000