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