extreme f(x)=x^2+1/x

Lösung

extrempunkte

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

Minimum (\frac{1}{3 2}, \frac{1}{2 ^{\frac{2}{3}}} + 32)

Schritte zur Lösung

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

Intervalle finden:

Absteigend

: - \infty < x < 0,

Absteigend

: 0 < x < \frac{1}{3 2},

Ansteigend

: \frac{1}{3 2} < x < \infty

Stecke

x = \frac{1}{3 2}

x^{2} + \frac{1}{x} : \frac{1}{2 ^{\frac{2}{3}}} + 32

Minimum (\frac{1}{3 2}, \frac{1}{2 ^{\frac{2}{3}}} + 32)

e x t re m e p (x) = 12 x^{4} + 15 x^{3} + a x^{2} - 69 x - 30

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

e x t re m e f (x, y) = 16 - (x - 2)^{2} - (y - 2)^{2}

e x t re m e f (x) = x^{4} - 18 x^{2} - 3

e x t re m e f (x) = x^{4} - 18 x^{2} + 5