extreme f(x)=x^2+3(x)((500)/(x^2))

Lösung

extrempunkte

f (x) = x^{2} + 3 (x) (\frac{500}{x ^{2}})

Minimum (536, 75 \cdot 6^{\frac{2}{3}})

Schritte zur Lösung

f^{'} (x) = 2 x - \frac{1500}{x ^{2}}

Intervalle finden:

Absteigend

: - \infty < x < 0,

Absteigend

: 0 < x < 536,

Ansteigend

: 536 < x < \infty

Stecke

x = 536

x^{2} + 3 x \frac{500}{x ^{2}} : 75 \cdot 6^{\frac{2}{3}}

Minimum (536, 75 \cdot 6^{\frac{2}{3}})

e x t re m e \frac{x - 3}{x ^{2} - 18 x + 81}

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

e x t re m e \frac{4 + x}{9 - x}, - 9 \leq x \leq 0

e x t re m e 333.7

e x t re m e f (x, y) = - 8 x^{2} - 3 y^{2} + 8 x - y + 2