extreme f(x)=3x+5x^{-1}

Lösung

extrempunkte

f (x) = 3 x + 5 x^{- 1}

Maximum (- \frac{5}{3}, - 215), Minimum (\frac{5}{3}, 215)

Schritte zur Lösung

f^{'} (x) = 3 - \frac{5}{x ^{2}}

Intervalle finden:

Ansteigend

: - \infty < x < - \frac{5}{3},

Absteigend

: - \frac{5}{3} < x < 0,

Absteigend

: 0 < x < \frac{5}{3},

Ansteigend

: \frac{5}{3} < x < \infty

Stecke

x = - \frac{5}{3}

3 x + 5 x^{- 1} : - 215

Maximum (- \frac{5}{3}, - 215)

Stecke

x = \frac{5}{3}

3 x + 5 x^{- 1} : 215

Minimum (\frac{5}{3}, 215)

Maximum (- \frac{5}{3}, - 215), Minimum (\frac{5}{3}, 215)

e x t re m e f (x) = (x - 1)^{5}

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

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

e x t re m e - x^{2} - 4 y^{2} + 8 x - 8 y - 16

e x t re m e f (x) = (x - 1)^{2} + y^{2} = 25