Question

Найдите точку минимума y=x^2+1000/x

Answer 1

y = x^2 + 1000/x
y ' = 2x - 1000/x^2 = (2x^3 - 1000)/x^2 = 2(x^3 - 500)/x^2 = 0
x^3 = 500
x0 = ∛500 ~ 8 (8^3 = 512)
y(x0) = ∛(500^2) + 1000/(∛500) = (500 + 1000)/(∛500) = 1500/(∛500) =
= 1500*∛(500^2)/500 = 3∛(250000) = 30∛250
Ответ: (∛500; 30∛250)