extreme f(x)=5x+3/x

Lösung

extrempunkte

f (x) = 5 x + \frac{3}{x}

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

Schritte zur Lösung

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

Intervalle finden:

Ansteigend

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

Absteigend

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

Absteigend

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

Ansteigend

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

Stecke

x = - \frac{3}{5}

5 x + \frac{3}{x} : - 215

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

Stecke

x = \frac{3}{5}

5 x + \frac{3}{x} : 215

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

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

e x t re m e f (x) = - x^{2} + 6 x - 4

e x t re m e f (x) = x^{2} - 12 x + 7

e x t re m e f (x) = - x^{3} + 3 x^{2} + 5

e x t re m e \frac{6 x ^{2}}{x ^{2} - 16}

e x t re m e f (x, y) = x^{2} - y^{2} + 6 x - 8 y + 25