2024 · Q1
A real number x is such that the sum of the number and four times its square is the least. What is that number?
Elementary MathematicsAlgebra
- A-0.625
- B-0.125
- C0.125
- D1
Explanation
Minimize f(x) = x + 4x². Differentiating, f′(x) = 1 + 8x = 0 gives x = −1/8 = −0.125, and f′′(x) = 8 > 0 confirms a minimum. Hence the least value of x + 4x² occurs at x = −0.125. This matches option B.