2019 · Q8
For x > 0, what is the minimum value of x + (x + 2)/(2x)?
Elementary MathematicsAlgebra
- A1
- B2
- C2½
- DCannot be determined
Explanation
f(x) = x + (x+2)/(2x) = x + 1/2 + 1/x for x > 0. By AM–GM, x + 1/x ≥ 2 with equality at x = 1. Hence f(x) ≥ 2 + 1/2 = 2½, and this minimum is attained at x = 1.