2019 · Q93
What is the maximum value of the expression 1/(x² + 5x + 10)?
Elementary MathematicsAlgebra
- A15/4
- B15/2
- C1
- D4/15
Explanation
The fraction is largest when its denominator is smallest. Completing the square: x² + 5x + 10 = (x + 5/2)² − 25/4 + 10 = (x + 2.5)² + 15/4 ≥ 15/4. Hence the maximum value is 1/(15/4) = 4/15. The answer is (D).