2019 · Q85
A real number x is such that (x - x²) is maximum. What is x equal to?
Elementary MathematicsAlgebra
- A-1.5
- B-0.5
- C0.5
- D1.5
Explanation
x − x² is a downward-opening parabola (equivalently, x − x² = 1/4 − (x − 1/2)² by completing the square). Its vertex — the maximum — is at x = 1/2 = 0.5, where the value is 0.25. The answer is (C).