Find a positive number such that the sum of the square of the number and its reciprocal is a minimum.

Answer 1

let the number be x, and the sum as stated be S

S = x^2 + 1/x
dS/dx = 2x - 1/x^2
= 0 for a max/min

2x = 1/x^2
2x^3 = 1
x^3 = 1/2
x = (1/2)^(1/3) or the cube root of 1/2