extreme 2x+1/x

Lösung

extrempunkte

2 x + \frac{1}{x}

Maximum (- \frac{1}{2}, - 22), Minimum (\frac{1}{2}, 22)

Schritte zur Lösung

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

Intervalle finden:

Ansteigend

: - \infty < x < - \frac{1}{2},

Absteigend

: - \frac{1}{2} < x < 0,

Absteigend

: 0 < x < \frac{1}{2},

Ansteigend

: \frac{1}{2} < x < \infty

Stecke

x = - \frac{1}{2}

2 x + \frac{1}{x} : - 22

Maximum (- \frac{1}{2}, - 22)

Stecke

x = \frac{1}{2}

2 x + \frac{1}{x} : 22

Minimum (\frac{1}{2}, 22)

Maximum (- \frac{1}{2}, - 22), Minimum (\frac{1}{2}, 22)

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

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

e x t re m e f (x, y) = x + 2 y

e x t re m e 5 sin^{2} (x)

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